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Zhu, Minghao, and Chunhua Wang. "A novel parallel chaotic system with greatly improved Lyapunov exponent and chaotic range." International Journal of Modern Physics B 34, no. 07 (March 17, 2020): 2050048. http://dx.doi.org/10.1142/s0217979220500484.
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Lyapunov exponent (LE), chaotic range and complexity are the key considerations of a discrete chaotic system. A dynamic chaotic system with larger LE and wider parameter space will result in better statistical performance that can be used to generate pseudo random sequences and applied to encryption fields. At the same time, the combination of simple chaotic maps can generate more excellent chaotic behavior. This paper proposes a newly combined chaotic system called Parallel Chaotic System (PCS). Multiple simple chaotic maps are paralleled to construct the novel system. In this system, LE and chaotic range can be improved as much as possible by setting additional parameters. Compared with the existing models made up of same seed maps, PCS is able to get better chaotic behavior by means of a simple structure at the same time. Performance evaluation emphasizes that the chaotic maps generated by PCS are more unpredictable with better complexity.
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Dai, Shengqiu, Kehui Sun, Shaobo He, and Wei Ai. "Complex Chaotic Attractor via Fractal Transformation." Entropy 21, no. 11 (November 14, 2019): 1115. http://dx.doi.org/10.3390/e21111115.
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Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement.
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Elizalde-Canales, Francisca Angélica, Iván De Jesus Rivas-Cambero, Lucio Fidel Rebolledo-Herrera, and Cesar Joel Camacho-Bello. "Pseudo-Random Bit Generator Using Chaotic Seed for Cryptographic Algorithm in Data Protection of Electric Power Consumption." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (April 1, 2019): 1399. http://dx.doi.org/10.11591/ijece.v9i2.pp1399-1409.
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<p>Cryptographic algorithms have played an important role in information security for protecting privacy. The literature provides evidence that many types of chaotic cryptosystems have been proposed. These chaotic systems encode information to obviate its orbital instability and ergodicity. In this work, a pseudo-random cryptographic generator algorithm with a symmetric key, based on chaotic functions, is proposed. Moreover, the algorithm exploits dynamic simplicity and synchronization to generate encryption sub-keys using unpredictable seeds, extracted from a chaotic zone, in order to increase their level of randomness. Also, it is applied to a simulated electrical energy consumption signal and implemented on a prototype, using low hardware resources, to measure physical variables; hence, the unpredictability degree was statistically analyzed using the resulting cryptogram. It is shown that the pseudo-random sequences produced by the cryptographic key generator have acceptable properties with respect to randomness, which are validated in this paper using National Institute of Standards and Technology (NIST) statistical tests. To complement the evaluation of the encrypted data, the Lena image is coded and its metrics are compared with those reported in the literature, yielding some useful results.</p>
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LOMBARDO, FERNANDO C., MARIO A. CASTAGNINO, and LUCA BOMBELLI. "FROM CLASSICAL CHAOS TO DECOHERENCE IN ROBERTSON–WALKER COSMOLOGY." Modern Physics Letters A 14, no. 07 (March 7, 1999): 539–47. http://dx.doi.org/10.1142/s0217732399000596.
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We analyze the relationship between classical chaos and particle creation in Robertson–Walker cosmological models with gravity coupled with a scalar field. Within our class of models chaos and particle production are seen to arise in the same cases. Particle production is viewed as the seed of decoherence, which enables the quantum to classical transition and ensures that the correspondence between the quantum and classically chaotic models will be valid.
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Chikkareddi, Vishwanath, Anurag Ghosh, Preksha Jagtap, Sahil Joshi, and Jeel Kanzaria. "Hybrid Image Encryption Technique Using Genetic Algorithm and Lorenz Chaotic System." ITM Web of Conferences 32 (2020): 03009. http://dx.doi.org/10.1051/itmconf/20203203009.
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One of the important application of image encryption is storing confidential and important images on a local device or a database in such a way that only the authorized party can view or perceive it. The current image encryption technique employs the genetic algorithm to increase confusion in the image, but compromises in time and space complexity. The other method employs chaos or pseudo random number generating systems which have fast and highly sensitive keys but fails to make the image sufficiently noisy and is risky due to its deterministic nature. We propose a technique which employs the non-deterministic, optimizing power of genetic algorithm and the space efficiency and key sensitivity of chaotic systems into a unified, efficient algorithm which will retain the merits of both the methods whereas tries to minimize their demerits in a software system. The encryption process proceeds in two steps, generating two keys. First, an encryption sequence is generated using Lorenz Chaotic system of differential equation. The seed values used are the user’s actual key having key sensitivity of 10-14. Second, the encrypted image’s genetic encryption sequence is generated which will result in an encrypted image with entropy value greater than 7.999 thus ensuring the image is very noisy. Proposed technique uses variations of Lorenz system seed sets to generate all random mutations and candidate solutions in Genetic encryption. Since only the seed sets leading to desired solution is stored, space efficiency is higher compared to storing the entire sequences. Using this image encryption technique we will ensure that the images are hidden securely under two layers of security, one chaotic and other non-deterministic.
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Datcu, Octaviana, Corina Macovei, and Radu Hobincu. "Chaos Based Cryptographic Pseudo-Random Number Generator Template with Dynamic State Change." Applied Sciences 10, no. 2 (January 8, 2020): 451. http://dx.doi.org/10.3390/app10020451.
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This article presents a configurable, high-throughput pseudo-random number generator template targeting cryptographic applications. The template is parameterized using a chaotic map that generates data, an entropy builder that is used to periodically change the parameters of the map and a parameter change interval, which is the number of iterations after which the entropy builder will change the generator’s parameters. The system is implemented in C++ and evaluated using the TestU01 and NIST RNG statistical tests. The same implementation is used for a stream cipher that can encrypt and decrypt PNG images. A Monte-Carlo analysis of the seed space was performed. Results show that for certain combinations of maps and entropy builders, more than 90% of initial states (seeds) tested pass all statistical randomness tests. Also, the throughput is large enough so that a 8 K color image can be encrypted in 2 s on a modern laptop CPU (exact specifications are given in the paper). The conclusion is that chaotic maps can be successfully used as a building block for cryptographic random number generators.
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JAWAD, LAHIEB MOHAMMED, and GHAZALI SULONG. "A Novel Dynamic Secret key Generation for an Efficient Image Encryption Algorithm." Modern Applied Science 9, no. 13 (November 30, 2015): 85. http://dx.doi.org/10.5539/mas.v9n13p85.
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<p>Today, the security of digital images is considered more and more essential and a strong secret key plays a major role in the image encryption. In this paper, a novel method for generating dynamic non-linear secret keys for a symmetric block cipher using XOR-operation is proposed. The dynamic non-linear secret keys generation is based on a combination of logistic and piecewise chaotic map methods with a new automatic creation of initial seed values. The automatic initial seed values creation depends on the development of a novel strategy for seeds creation based on sunflower spiral points. The experimental results indicate that the proposed key generator algorithm has the advantage of large key space with a safety protection of brute force attack. Therefore, the performance analysis of image encryption reveals a correlation coefficient of about (-0.0001) and entropy greater than (7.9978). Furthermore, the results show high security for encryption based on strong dynamic secret key properties.</p>
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Machicao, Jeaneth, Odemir M. Bruno, and Murilo S. Baptista. "Zooming into chaos as a pathway for the creation of a fast, light and reliable cryptosystem." Nonlinear Dynamics 104, no. 1 (February 22, 2021): 753–64. http://dx.doi.org/10.1007/s11071-021-06280-y.
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AbstractMotivated by today’s huge volume of data that needs to be handled in secrecy, there is a wish to develop not only fast and light but also reliably secure cryptosystems. Chaos allows for the creation of pseudo-random numbers (PRNs) by low-dimensional transformations that need to be applied only a small number of times. These two properties may translate into a chaos-based cryptosystem that is both fast (short running time) and light (little computational effort). What we propose here is an approach to generate PRNs—and consequently digital secret keys—that can serve as a seed for an enhanced chaos-based cryptosystem. We use low-dimensional chaotic maps to quickly generate PRNs that have little correlation, and then, we quickly (“fast”) enhance secrecy by several orders (“reliability”) with very little computational cost (“light”) by simply looking at the less significant digits of the initial chaotic trajectory. This paper demonstrates this idea with rigor, by showing that a transformation applied a small number of times to chaotic trajectories significantly increases its entropy and Lyapunov exponents, as a consequence of the smoothing out of the probability density towards a uniform distribution.
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Rempel, Erico L., Abraham C. L. Chian, Axel Brandenburg, Pablo R. Muñoz, and Shawn C. Shadden. "Coherent structures and the saturation of a nonlinear dynamo." Journal of Fluid Mechanics 729 (July 19, 2013): 309–29. http://dx.doi.org/10.1017/jfm.2013.290.
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AbstractEulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean-field dynamo, produced by direct numerical simulations of the three-dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied: the kinematic stage, where a seed magnetic field undergoes exponential growth; and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, in addition to providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite-time Lyapunov exponents is compared with a recently developed method called function $M$. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.
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Jarjar, Mohamed, Said Hraoui, Said Najah, and Khalid Zenkouar. "Instructions New Technology of Color Image Encryption Based Two Improved Vigenere Laps Separated by a Genetic Mutation." International Journal of Safety and Security Engineering 11, no. 5 (October 31, 2021): 605–13. http://dx.doi.org/10.18280/ijsse.110512.
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This document traces the development of a new cryptosystem using two circuits ensured by a deep Vigenere classical technique improvement. This new technique employs several dynamic substitutions matrices attached to chaotic replacement functions; whose construction will be detailed. The first round will start by modifying the seed pixels based on the initial values calculated from the original image, and will be infected through the chaotic map used to overcome the uniform image problem, followed by the injection of Vigenere technology improvements. The output vector will be subdivided into three sized blocks for future application of deeply improved genetic mutations to better adapt to medicine and color image encryption. The second round will increase the complexity of the attack and improve the installed systems. Simulations performed on a large number of images of different sizes and formats ensure that our approach is not exposed to known attacks.
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Nguyen, Ngoc, Georges Kaddoum, Fabio Pareschi, Riccardo Rovatti, and Gianluca Setti. "A fully CMOS true random number generator based on hidden attractor hyperchaotic system." Nonlinear Dynamics 102, no. 4 (October 31, 2020): 2887–904. http://dx.doi.org/10.1007/s11071-020-06017-3.
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AbstractLow-power devices used in Internet-of-things networks have been short of security due to the high power consumption of random number generators. This paper presents a low-power hyperchaos-based true random number generator, which is highly recommended for secure communications. The proposed system, which is based on a four-dimensional chaotic system with hidden attractors and oscillators, exhibits rich dynamics. Numerical analysis is provided to verify the dynamic characteristics of the proposed system. A fully customized circuit is deployed using 130 nm CMOS technology to enable integration into low-power devices. Four output signals are used to seed a SHIFT-XOR-based chaotic data post-processing to generate random bit output. The chip prototype was simulated and tested at 100 MHz sampling frequency. The hyperchaotic circuit consumes a maximum of 980 $$\upmu $$ μ W in generating chaotic signals while dissipates a static current of 623 $$\upmu $$ μ A. Moreover, the proposed system provides ready-to-use binary random bit sequences which have passed the well-known statistical randomness test suite NIST SP800-22. The proposed novel system design and its circuit implementation provide a best energy efficiency of 4.37 pJ/b at a maximum sampling frequency of 100 MHz.
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Hemed, Ayser A., Zainab Rashid Ghayib, and Hayfa Ghazi Rashid. "Controlling a chaotic anti-synchronized oscillator by a phase interplayed optical injected seed with an FBG sensor." Journal of Physics: Conference Series 1963, no. 1 (July 1, 2021): 012063. http://dx.doi.org/10.1088/1742-6596/1963/1/012063.
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Zhao, Huan, Shaofang He, Zuo Chen, and Xixiang Zhang. "Dual Key Speech Encryption Algorithm Based Underdetermined BSS." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/974735.
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When the number of the mixed signals is less than that of the source signals, the underdetermined blind source separation (BSS) is a significant difficult problem. Due to the fact that the great amount data of speech communications and real-time communication has been required, we utilize the intractability of the underdetermined BSS problem to present a dual key speech encryption method. The original speech is mixed with dual key signals which consist of random key signals (one-time pad) generated by secret seed and chaotic signals generated from chaotic system. In the decryption process, approximate calculation is used to recover the original speech signals. The proposed algorithm for speech signals encryption can resist traditional attacks against the encryption system, and owing to approximate calculation, decryption becomes faster and more accurate. It is demonstrated that the proposed method has high level of security and can recover the original signals quickly and efficiently yet maintaining excellent audio quality.
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LUI, OI-YAN, CHING-HUNG YUEN, and KWOK-WO WONG. "A PSEUDO-RANDOM NUMBER GENERATOR EMPLOYING MULTIPLE RÉNYI MAPS." International Journal of Modern Physics C 24, no. 11 (October 14, 2013): 1350079. http://dx.doi.org/10.1142/s0129183113500794.
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The increasing risk along with the drastic development of multimedia data transmission has raised a big concern on data security. A good pseudo-random number generator is an essential tool in cryptography. In this paper, we propose a novel pseudo-random number generator based on the controlled combination of the outputs of several digitized chaotic Rényi maps. The generated pseudo-random sequences have passed both the NIST 800-22 Revision 1a and the DIEHARD tests. Moreover, simulation results show that the proposed pseudo-random number generator requires less operation time than existing generators and is highly sensitive to the seed.
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Tsytsiura, Yaroslav. "SELECTION OF EFFECTIVE SOFTWARE FOR THE ANALYSIS OF THE FRACTIONAL COMPOSITION OF THE CHAOTIC SEED LAYER USING THE EXAMPLE OF OILSEED RADISH." Engenharia Agrícola 41, no. 2 (April 2021): 161–70. http://dx.doi.org/10.1590/1809-4430-eng.agric.v41n2p161-170/2021.
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Vincent, Lionel, W. Scott Shambaugh, and Eva Kanso. "Holes stabilize freely falling coins." Journal of Fluid Mechanics 801 (July 21, 2016): 250–59. http://dx.doi.org/10.1017/jfm.2016.432.
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The free fall of heavy bodies in a viscous fluid medium is a problem of interest to many engineering and scientific disciplines, including the study of unpowered flight and seed dispersal. The falling behaviour of coins and thin discs in particular has been categorized into one of four distinct modes; steady, fluttering, chaotic or tumbling, depending on the moment of inertia and Reynolds number. This paper investigates, through a carefully designed experiment, the falling dynamics of thin discs with central holes. The effects of the central hole on the disc’s motion is characterized for a range of Reynolds number, moments of inertia and inner to outer diameter ratio. By increasing this ratio, that is, the hole size, the disc is found to transition from tumbling to chaotic then fluttering at values of the moment of inertia not predicted by the falling modes of whole discs. This transition from tumbling to fluttering with increased hole size is viewed as a stabilization process. Flow visualization of the wake behind annular discs shows the presence of a vortex ring at the disc’s outer edge, as in the case of whole discs, and an additional counter-rotating vortex ring at the disc’s inner edge. The inner vortex ring is responsible for stabilizing the disc’s falling motion. These findings have significant implications on the development of design principles for engineered robotic systems in free flight, and may shed light on the stability of gliding animals.
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Czarnecka, Bożena. "The dynamics of the population of a steppe perennial Senecio macrophyllus M.BIEB. during xerothermic grassland overgrowing." Acta Societatis Botanicorum Poloniae 78, no. 3 (2011): 247–56. http://dx.doi.org/10.5586/asbp.2009.032.
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The study aimed to determine the long-term changes of the <em>Senecio macrophyllus</em> M.BIEB. population traits: the abundance, reproduction mode, individual fecundity, seed rain and recruitment of new genets in the course of xerothermic grassland overgrowing. The study had also the applied goal: to estimate the chances of "special care" species to survive in the changing environment without management regime for the maintenance of grassland. The model object was the island population of large-leaved ragwort on Biała Góra (the White Mountain) near Tomaszów Lubelski, South-East Poland. To achieve these aims I used the following sets of data: phytosociological relev,s made in plant communities in an interval of 16-18 years; repeated elaboration of the numbers and life-stage structure of the population, both by non-surface and surface method; observation of plants<sup>,</sup> life cycle in 50 labelled genets; population reproduction and seed rain amounts. The area of an open xerothermic grassland decreased due to the process of overgrowing by bushes which was accompanied by the increasing coverage of forest and meadow herbs as well as monocotyledons, mainly <em>Brachypodium pinnatum</em> and <em>Calamagrostis epigejos</em>. The abundance of the <em>S. macrophyllus</em> population noticable diminished. The flowering mode has been changing during years from an oscillation to a chaotic type which caused the significant decreasing of the individual fecundity, population reproduction and seed rain. In last years it was reflected in the interruption of juveniles’ recruitment.
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Poon, Sanson T. S., Richard P. Nelson, and Gavin A. L. Coleman. "In situ formation of hot Jupiters with companion super-Earths." Monthly Notices of the Royal Astronomical Society 505, no. 2 (May 21, 2021): 2500–2516. http://dx.doi.org/10.1093/mnras/stab1466.
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ABSTRACT Observations have confirmed the existence of multiple-planet systems containing a hot Jupiter and smaller planetary companions. Examples include WASP-47, Kepler-730, and TOI-1130. We examine the plausibility of forming such systems in situ using N-body simulations that include a realistic treatment of collisions, an evolving protoplanetary disc, and eccentricity/inclination damping of planetary embryos. Initial conditions are constructed using two different models for the core of the giant planet: a ‘seed-model’ and an ‘equal-mass-model’. The former has a more massive protoplanet placed among multiple small embryos in a compact configuration. The latter consists only of equal-mass embryos. Simulations of the seed-model lead to the formation of systems containing a hot Jupiter and super-Earths. The evolution consistently follows four distinct phases: early giant impacts; runaway gas accretion on to the seed protoplanet; disc damping-dominated evolution of the embryos orbiting exterior to the giant; a late chaotic phase after dispersal of the gas disc. Approximately 1 per cent of the equal-mass simulations form a giant and follow the same four-phase evolution. Synthetic transit observations of the equal-mass simulations provide an occurrence rate of 0.26 per cent for systems containing a hot Jupiter and an inner super-Earth, similar to the 0.2 per cent occurrence rate from actual transit surveys, but simulated hot Jupiters are rarely detected as single transiting planets, in disagreement with observations. A subset of our simulations form two close-in giants, similar to the WASP-148 system. The scenario explored here provides a viable pathway for forming systems with unusual architectures, but does not apply to the majority of hot Jupiters.
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Li, Xiaocan, Brahmananda Dasgupta, and Gang Li. "Energization of charged particle in a time-dependent chaotic magnetic field with an implication of the production of seed particles in solar energetic particle events." Advances in Space Research 53, no. 8 (April 2014): 1153–61. http://dx.doi.org/10.1016/j.asr.2014.01.008.
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BLINOV, L. M., G. CHIDICHIMO, G. CIPPARRONE, P. PAGLIUSI, and T. RUGIERO. "BAND NARROWING AND GAIN SPECTRA OF LASER DYE SOLUTIONS WITH SCATTERING TiO2 NANOPARTICLES." Journal of Nonlinear Optical Physics & Materials 17, no. 01 (March 2008): 71–83. http://dx.doi.org/10.1142/s0218863508003981.
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The spectra of amplified spontaneous emission (ASE) intensity and gain have been measured for solutions of laser dye Rhodamine-640 in glycerin with light scattering TiO 2 nanoparticles. Such solutions typically manifest random lasing in backscattering geometry. In this work, the conventional transverse pump geometry is used, and the ASE gain spectra are measured using a variation of the length of the illuminated (pumped) stripe. In this geometry, with increasing concentration of nanoparticles, the "unidirectional" gain along the stripe decreases dramatically. At the same time, strong narrowing of the ASE bandwidth is observed even in the absence of net gain. The experimental results help one to understand the role of the scattering particles in the light amplification. On the one hand, the particles increase a zigzag type of the light path within the amplifying medium, which results in bandwidth narrowing and strong amplification of chaotic light beams. On the other hand, the amplification of a seed beam propagating in a selected direction is dramatically suppressed. The results are discussed using simple modeling of ASE amplification and qualitative arguments.
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Gaffar, Achmad Fanany Onnilita, Rheo Malani, and Arief Bramanto Wicaksono Putra. "Magic cube puzzle approach for image encryption." International Journal of Advances in Intelligent Informatics 6, no. 3 (November 6, 2020): 290. http://dx.doi.org/10.26555/ijain.v6i3.422.
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In principle, the image encryption algorithm produces an encrypted image. The encrypted image is composed of arbitrary patterns that do not provide any clues about the plain image and its cipher key. Ideally, the encrypted image is entirely independent of its plain image. Many functions can be used to achieve this goal. Based on the functions used, image encryption techniques are categorized into: (1) Block-based; (2) Chaotic-based; (3) Transformation-based; (4) Conventional-based; and (5) Miscellaneous based. This study proposes a magic cube puzzle approach to encrypt an 8-bit grayscale image. This approach transforms a plain image into a particular size magic cube puzzle, which is consists of a set of blocks. The magic cube puzzle algorithm will diffuse the pixels of the plain image as in a Rubik’s Cube game, by rotating each block in a particular direction called the transposition orientation. The block’s transposition orientation is used as the key seed, while the generation of the cipher key uses a random permutation of the key seed with a certain key length. Several performance metrics have been used to assess the goals, and the results have been compared to several standard encryption methods. This study showed that the proposed method was better than the other methods, except for entropy metrics. For further studies, modification of the method will be carried out in such a way as to be able to increase its entropy value to very close to 8 and its application to true color images. In essence, the magic cube puzzle approach has a large space for pixel diffusion that is possibly supposed to get bigger as a series of data has transformed into several magic cubes. Then, each magic cube has transposed with a different technique. This proposed approach is expected to add to a wealth of knowledge in the field of data encryption.
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Ignatenko, Roman V., Natalia A. Galibina, and Boris B. Raevsky. "Cytogenetic evaluation of Pinus sylvestris L. in the European North of Russia (Republic of Karelia)." Turczaninowia 25, no. 1 (March 30, 2022): 73–85. http://dx.doi.org/10.14258/turczaninowia.25.1.7.
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This article presents the results of cytogenetic analysis of the Pinus sylvestris L. seed progeny from 5 populations growing in the boreal forests of the European North of Russia (Republic of Karelia). Based on the study of plants karyotype, it was found that in addition to diploid cells some seedlings contained single tetraploid and aneuploid cells. Mainly, mixoploid plants were found in Sheltozerskoye and Ambarnskoye forest divisions. It is important to note that these populations were characterized by high values of such indicators as the frequency of mitotic pathologies at the metaphase and ana-telophase stages (5.3 ± 0.6 and 7.1 ± 0.6 % respectively), as well as the proportion of cells with micronuclei (0.2 ± 0.06 and 0.1 ± 0.04 % respectively) in the root meristem of Pinus sylvestris. However, despite data received, seeds from Sheltozersky and Ambarnsky forest divisions had high germination values. Nine types of chromosome aberrations were found due to the analysis: fragmentation, bridges, ring chromosomes, lagging, chromosome leading, isolation, multipolar and chaotic chromosome divergence, complex (multiple) disorders. In most of the seedlings studied, the most common pathology was chromosome overrun. In addition, the study showed that bridges proportion in the total disturbances’ spectrum at the ana-telophase stages of mitosis increases by ~ 3.5 times in Pinus sylvestris populations growing in the northern taiga subzone compared to the middle taiga populations. In most of the seedlings studied, the most common pathology was chromosome overrun. Thus, the use of a cytogenetic test made it possible to evaluate the state of Pinus sylvestris genome from different populations in the European North of Russia and to identify responses aimed at plant adaptation to environmental conditions at the cellular level.
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Das, Arpan, Dominik R. G. Schleicher, Nathan W. C. Leigh, and Tjarda C. N. Boekholt. "Formation of supermassive black hole seeds in nuclear star clusters via gas accretion and runaway collisions." Monthly Notices of the Royal Astronomical Society 503, no. 1 (February 11, 2021): 1051–69. http://dx.doi.org/10.1093/mnras/stab402.
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ABSTRACT More than 200 supermassive black holes (SMBHs) of masses $\gtrsim 10^9\, \mathrm{M_{\odot }}$ have been discovered at z ≳ 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ into seed black holes which could grow upto few times $10^9\, \mathrm{M_{\odot }}$ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealized N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi–Hoyle–Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion time-scale remains considerably shorter than the time-scale for collisions with the most massive object (MMO). However, overall the time-scale for collisions between any two stars in the cluster can become comparable or shorter than the accretion time-scale, hence collisions still play a crucial role in determining the final mass of the SMSs. We find that the problem is highly sensitive to the initial conditions and our assumed recipe for the accretion, due to the highly chaotic nature of the problem. The key variables that determine the mass growth mechanism are the mass of the MMO and the gas reservoir that is available for the accretion. Depending on different conditions, SMSs of masses $\sim 10^{3}{-}10^{5} \, \mathrm{M_{\odot }}$ can form for all three accretion scenarios considered in this work.
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Eaves, T. S., and C. P. Caulfield. "Disruption of states by a stable stratification." Journal of Fluid Mechanics 784 (November 6, 2015): 548–64. http://dx.doi.org/10.1017/jfm.2015.596.
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We identify ‘minimal seeds’ for turbulence, i.e. initial conditions of the smallest possible total perturbation energy density $E_{c}$ that trigger turbulence from the laminar state, in stratified plane Couette flow, the flow between two horizontal plates of separation $2H$, moving with relative velocity $2{\rm\Delta}U$, across which a constant density difference $2{\rm\Delta}{\it\rho}$ from a reference density ${\it\rho}_{r}$ is maintained. To find minimal seeds, we use the ‘direct-adjoint-looping’ (DAL) method for finding nonlinear optimal perturbations that optimise the time-averaged total dissipation of energy in the flow. These minimal seeds are located adjacent to the edge manifold, the manifold in state space that separates trajectories which transition to turbulence from those which eventually decay to the laminar state. The edge manifold is also the stable manifold of the system’s ‘edge state’. Therefore, the trajectories from the minimal seed initial conditions spend a large amount of time in the vicinity of some states: the edge state; another state contained within the edge manifold; or even in dynamically slowly varying regions of the edge manifold, allowing us to investigate the effects of a stable stratification on any coherent structures associated with such states. In unstratified plane Couette flow, these coherent structures are manifestations of the self-sustaining process (SSP) deduced on physical grounds by Waleffe (Phys. Fluids, vol. 9, 1997, pp. 883–900), or equivalently finite Reynolds number solutions of the vortex–wave interaction (VWI) asymptotic equations initially derived mathematically by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666). The stratified coherent states we identify at moderate Reynolds number display an altered form from their unstratified counterparts for bulk Richardson numbers $\mathit{Ri}_{B}=g{\rm\Delta}{\it\rho}H/({\it\rho}_{r}{\rm\Delta}U^{2})=O(\mathit{Re}^{-1})$, and exhibit chaotic motion for larger $\mathit{Ri}_{B}$. We demonstrate that at hith Reynolds number the suppression of vertical motions by stratification strongly disrupts input from the waves to the roll velocity structures, thus preventing the waves from reinforcing the viscously decaying roll structures adequately, when $\mathit{Ri}_{B}=O(\mathit{Re}^{-2})$.
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Kasianenko, V., and N. Kotenko. "THE ISSUE SUSTAINABILITY STARTUP FINANCING DURING THE LIFE CYCLE." Vìsnik Sumsʹkogo deržavnogo unìversitetu, no. 3 (2019): 117–23. http://dx.doi.org/10.21272/1817-9215.2019.3-15.
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Around the world, lack of funds and poor choice of investors are causing the death of the vast majority of startups right from the very beginning of their existence. Research on problems and prospects for start-ups in Ukraine focuses primarily on the search and improvement of macroeconomic tools and methods, while foreign resources offer specific practical recommendations that are chaotic, aimed at solving "point" problems, and do not contain a generalized methodological framework. The article clarifies the meaningful characteristics of startups - time constraints (10 years), stages of business cycles (pre-seed, seed, startup, growth, expansion, maturity, and possible exit), and fundraising. An analysis of the structure of sources of funding for start-ups in the European Union has shown that most founders rely on their own resources and the help of friends and relatives; the least involved fundraising tools are loans, IPOs, and ISOs. On the other hand, business angels and venture capital are active mainly in the "adult" stages of startup development. These findings enabled the authors to systematize the fundraising sources according to the stages of the startup development and to identify the vulnerable elements that threaten the sustainability of the fundraising startups, which is defined as the ability to implement the program or project and maintain the positive results in the long run. An analysis of approaches to assessing the level of sustainability of funding has led to the conclusion that in order to fundraise effectively for startups, it is important not only to diversify sources of funding but to select the right types of resources that will meet the project's mission and founders' expectations. In view of this, the authors propose to divide all types of fundraising sources into three categories: internal, supportive or neutral, and external. Such a division, supported by the motivational characteristics of the startup for its founder, allows authors to take into account the individual constraints and capabilities of each source and maximize the benefit and sustainability of funding. The work identifies the most vulnerable interstage transition in the startup lifecycle and proposes to use an additional source of fundraising, to support the local community, to ensure financial sustainability. Keywords: startup, startup lifecycle, fundraising, sustainability of fundraising, public funding.
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Kruelle, C. A., A. Kittel, J. Peinke, R. Richter, and R. P. Huebener. "Chaotic billiards seen as mirror cabinets." Physica D: Nonlinear Phenomena 102, no. 3-4 (April 1997): 227–33. http://dx.doi.org/10.1016/s0167-2789(96)00241-2.
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Krause, F. "Stellar Dynamos." International Astronomical Union Colloquium 137 (1993): 578–90. http://dx.doi.org/10.1017/s0252921100018509.
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AbstractEnergy is transported from the central regions of a star to its surface. Generally this transport is in certain layers carried on by convective motions. Because of the structure, which these motions have due to the influence of the overall rotation, the star becomes electromagnetically unstable, i.e. a large magnetic field grows from small seed fields as a result of the dynamo process. The internal structure, especially the symmetries of a star, will be, at least to some extend, reflected by the spatial structure and the time behaviour of the excited magnetic field. In this sense observations of the magnetic field on a surface of a star and the related activity phenomena can provide insight in the internal structure of the star, since characteristic parameters like thickness of the convection zone, mixing length, turnover time, profile of the differential rotation, etc. strongly influence the dynamo process.The actual magnetic field of a star is a product of a nonlinear process. Models elaborated on the kinematical (i.e. linear) level provide insight in the excitation conditions and the linear field modes. The marginal mode, i.e. the mode which is easiest to excite, reflects properties of the nonlinear solution in case the system operates not far from the margin to the dynamo unstable region. Here the solutions show symmetries with respect to the axis of rotation and the equatorial plane, properties which are, for example, to a large extend fulfilled for the solar average magnetic field. For systems operating far from this margin irregular or even chaotic behaviour has to be expected. From observations there is a strong indication that these theoretical possibilities find their realizations within the sample of late-type stars.
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THOMAS, R. "DETERMINISTIC CHAOS SEEN IN TERMS OF FEEDBACK CIRCUITS: ANALYSIS, SYNTHESIS, "LABYRINTH CHAOS"." International Journal of Bifurcation and Chaos 09, no. 10 (October 1999): 1889–905. http://dx.doi.org/10.1142/s0218127499001383.
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This paper aims to show how complex nonlinear dynamic systems can be classified, analyzed and synthesized in terms of feedback circuits. The Rössler equations for deterministic chaos are revisited and generalized in this perspective. It is shown that once a proper set of feedback circuits is present in the Jacobian matrix of the system, the chaotic character of trajectories is remarkably robust versus changes in the nature of the nonlinearities. "Labyrinth chaos", whereby simple differential systems generate large lattices of many unstable steady states embedded in a chaotic attractor, is constructed using this technique. In the limit case of a single three-element circuit without diagonal elements, one finds systems possessing an infinite lattice of unstable steady states between which trajectories percolate in a deterministic chaotic way.
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Garcia-Bosque, M., C. Sánchez-Azqueta, and S. Celma. "Sensor-Based Seeds for a Chaotic Stream Cipher." Procedia Engineering 168 (2016): 1663–66. http://dx.doi.org/10.1016/j.proeng.2016.11.485.
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Kruelle, C. A., A. Kittel, and R. P. Huebener. "Nonintegrable Stadium Billiard seen as Mirror Cabinet." Zeitschrift für Naturforschung A 48, no. 10 (October 1, 1993): 1039–40. http://dx.doi.org/10.1515/zna-1993-1013.
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Abstract The Bunimovich stadium billiard is treated as a mirror cabinet seen from inside. The resulting system of virtual images of the mirror walls reveals a fractional structure which corresponds to the chaotic trajectories of light rays or billiard balls inside the stadium.
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Wang, Tianyi. "Classification of Chaotic Behaviors in Jerky Dynamical Systems." Complex Systems 30, no. 1 (February 15, 2021): 93–110. http://dx.doi.org/10.25088/complexsystems.30.1.93.
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Differential equations are widely used to model systems that change over time, some of which exhibit chaotic behaviors. This paper proposes two new methods to classify these behaviors that are utilized by a supervised machine learning algorithm. Dissipative chaotic systems, in contrast to conservative chaotic systems, seem to follow a certain visual pattern. Also, the machine learning program written in the Wolfram Language is utilized to classify chaotic behavior with an accuracy around 99.1±1.1%.
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Cherubini, S., and P. De Palma. "Minimal-energy perturbations rapidly approaching the edge state in Couette flow." Journal of Fluid Mechanics 764 (January 20, 2015): 572–98. http://dx.doi.org/10.1017/jfm.2014.716.
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AbstractTransition to turbulence in shear flows is often subcritical, thus the dynamics of the flow strongly depends on the shape and amplitude of the perturbation of the laminar state. In the state space, initial perturbations which directly relaminarize are separated from those that go through a chaotic trajectory by a hypersurface having a very small number of unstable dimensions, known as the edge of chaos. Even for the simple case of plane Couette flow in a small domain, the edge of chaos is characterized by a fractal, folded structure. Thus, the problem of determining the threshold energy to trigger subcritical transition consists in finding the states on this complex hypersurface with minimal distance (in the energy norm) from the laminar state. In this work we have investigated the minimal-energy regions of the edge of chaos, by developing a minimization method looking for the minimal-energy perturbations capable of approaching the edge state (within a prescribed tolerance) in a finite target time $T$. For sufficiently small target times, the value of the minimal energy has been found to vary with $T$ following a power law, whose best fit is given by $E_{min}\propto T^{-1.75}$. For large values of $T$, the minimal energy achieves a constant value which corresponds to the energy of the minimal seed, namely the perturbation of minimal energy asymptotically approaching the edge state (Rabin et al., J. Fluid Mech., vol. 738, 2012, R1). For $T\geqslant 40$, all of the symmetries of the edge state are broken and the minimal perturbation appears to be localized in space with a basic structure composed of scattered patches of streamwise velocity with inclined streamwise vortices on their flanks. Finally, we have found that minimal perturbations originate in a small low-energy zone of the state space and follow very fast similar trajectories towards the edge state. Such trajectories are very different from those of linear optimal disturbances, which need much higher initial amplitudes to approach the edge state. The time evolution of these minimal perturbations represents the most efficient path to subcritical transition for Couette flow.
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Anees, Amir, and Iqtadar Hussain. "A Novel Method to Identify Initial Values of Chaotic Maps in Cybersecurity." Symmetry 11, no. 2 (January 27, 2019): 140. http://dx.doi.org/10.3390/sym11020140.
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Chaos theory has applications in several disciplines and is focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic dynamics are the impromptu behavior displayed by some nonlinear dynamical frameworks and have been used as a source of diffusion in cybersecurity for more than two decades. With the addition of chaos, the overall strength of communication security systems can be increased, as seen in recent proposals. However, there is a major drawback of using chaos in communication security systems. Chaotic communication security systems rely on private keys, which are the initial values and parameters of chaotic systems. This paper shows that these chaotic communication security systems can be broken by identifying those initial values through the statistical analysis of standard deviation and variance. The proposed analyses are done on the chaotic sequences of Lorenz chaotic system and Logistic chaotic map and show that the initial values and parameters, which serve as security keys, can be retrieved and broken in short computer times. Furthermore, the proposed model of identifying the initial values can also be applied on other chaotic maps as well.
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Kay, Leslie M. "Chaotic itinerancy: Insufficient perceptual evidence." Behavioral and Brain Sciences 24, no. 5 (October 2001): 819–20. http://dx.doi.org/10.1017/s0140525x01320095.
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Chaotic itinerancy is useful for illustrating transitions in attractor dynamics seen in the olfactory system. Cantor coding is a good model for information processing, but so far it lacks perceptual proof. The theories presented provide a large step toward bridging the use of chaos as an interpretive tool and hard examination of chaotic neural activity during perception.
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Hassan, Sk Sarif, Moole Parameswar Reddy, and Ranjeet Kumar Rout. "Dynamics of the Modified n-Degree Lorenz System." Applied Mathematics and Nonlinear Sciences 4, no. 2 (August 22, 2019): 315–30. http://dx.doi.org/10.2478/amns.2019.2.00028.
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AbstractThe Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.
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Varan, Metin, Akif Akgül, Emre Güleryüz, and Kasım Serbest. "Synchronisation and Circuit Realisation of Chaotic Hartley System." Zeitschrift für Naturforschung A 73, no. 6 (June 27, 2018): 521–31. http://dx.doi.org/10.1515/zna-2018-0027.
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AbstractHartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.
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GALVANETTO, U. "UNUSUAL CHAOTIC ATTRACTORS IN NONSMOOTH DYNAMIC SYSTEMS." International Journal of Bifurcation and Chaos 15, no. 12 (December 2005): 4081–86. http://dx.doi.org/10.1142/s0218127405014520.
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The present paper describes an unusual example of chaotic motion occurring in a nonsmooth mechanical system affected by dry friction. The mechanical system generates one-dimensional maps the orbits of which seem to exhibit sensitive dependence on initial conditions only in an extremely small set of their field of definition. The chaotic attractor is composed of zones characterized by very different rates of divergence of nearby orbits: in a large portion of the chaotic attractor the system motion follows a regular pattern whereas the more usual irregular motion affects only a small portion of the attractor. The irregular phase reintroduces the orbit in the regular zone and the sequence is repeated. The Lyapunov exponent of the map is computed to characterize the steady state motions and confirm their chaotic nature.
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Newth, Gerald. "World order from chaotic beginnings." Mathematical Gazette 88, no. 511 (March 2004): 39–45. http://dx.doi.org/10.1017/s0025557200174212.
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This article explains the variety of patterns seen in sequences defined by for bilinear functions of the form . The initial confusion of very different patterns can be understood by generalising from the real numbers to the whole complex plane, and simplified further by projecting each number from the plane onto the surface of a sphere. The sphere is finally projected onto a Mercator map on which the iterative sequences take on the simplest possible pattern, creating a link with the problem of rhumb-line navigation. The examples given below are typical, and should first be tried as a reminder of what can happen.
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Cole-Kodikara, Elizabeth M., Maarit J. Käpylä, Jyri J. Lehtinen, Thomas Hackman, Ilya V. Ilyin, Nikolai Piskunov, and Oleg Kochukhov. "Spot evolution on LQ Hya from 2006–2017: temperature maps based on SOFIN and FIES data." Astronomy & Astrophysics 629 (September 2019): A120. http://dx.doi.org/10.1051/0004-6361/201935729.
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Context. LQ Hya is one of the most frequently studied young solar analogue stars. Recently, it has been observed to show intriguing behaviour when analysing long-term photometry. For instance, from 2003–2009, a coherent spot structure migrating in the rotational frame was reported by various authors. However, ever since, the star has entered a chaotic state where coherent structures seem to have disappeared and rapid phase jumps of the photometric minima occur irregularly over time. Aims. LQ Hya is one of the stars included in the SOFIN/FIES long-term monitoring campaign extending over 25 yr. Here, we publish new temperature maps for the star during 2006–2017, covering the chaotic state of the star. Methods. We used a Doppler imaging technique to derive surface temperature maps from high-resolution spectra. Results. From the mean temperatures of the Doppler maps, we see a weak but systematic increase in the surface temperature of the star. This is consistent with the simultaneously increasing photometric magnitude. During nearly all observing seasons, we see a high-latitude spot structure which is clearly non-axisymmetric. The phase behaviour of this structure is very chaotic but agrees reasonably well with the photometry. Equatorial spots are also frequently seen, but we interpret many of them to be artefacts due to the poor to moderate phase coverage. Conclusions. Even during the chaotic phase of the star, the spot topology has remained very similar to the higher activity epochs with more coherent and long-lived spot structures. In particular, we see high-latitude and equatorial spot activity, the mid latitude range still being most often void of spots. We interpret the erratic jumps and drifts in phase of the photometric minima to be caused by changes in the high-latitude spot structure rather than the equatorial spots.
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COHEN, M. E., D. L. HUDSON, M. F. ANDERSON, and P. C. DEEDWANIA. "A CONJECTURE TO THE SOLUTION OF THE CONTINUOUS LOGISTIC EQUATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 02, no. 04 (December 1994): 445–61. http://dx.doi.org/10.1142/s0218488594000353.
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Chaotic models as a rule are based on nonlinear recursive discrete equations, often illustrated by the logistic equation. In this paper, a conjecture is presented that gives an approximate solution to the continuous logistic equation. It is shown that if certain chaotic models are viewed as continuous rather than discrete, the strict borderline mathematical concept of the onset of chaos no longer retains its importance in some practical problems. In fact, it is more important to look at the degree of chaos, as illustrated in two medical problems dealing with blood flow and heart rate variability. The chaotic modeling approach is seen to be useful in analyzing experimental data.
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Mrgole, Anamarija L., and Drago Sever. "Incorporation of Duffing Oscillator and Wigner-Ville Distribution in Traffic Flow Prediction." PROMET - Traffic&Transportation 29, no. 1 (February 6, 2017): 13–22. http://dx.doi.org/10.7307/ptt.v29i1.2116.
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The main purpose of this study was to investigate the use of various chaotic pattern recognition methods for traffic flow prediction. Traffic flow is a variable, dynamic and complex system, which is non-linear and unpredictable. The emergence of traffic flow congestion in road traffic is estimated when the traffic load on a specific section of the road in a specific time period is close to exceeding the capacity of the road infrastructure. Under certain conditions, it can be seen in concentrating chaotic traffic flow patterns. The literature review of traffic flow theory and its connection with chaotic features implies that this kind of method has great theoretical and practical value. Researched methods of identifying chaos in traffic flow have shown certain restrictions in their techniques but have suggested guidelines for improving the identification of chaotic parameters in traffic flow. The proposed new method of forecasting congestion in traffic flow uses Wigner-Ville frequency distribution. This method enables the display of a chaotic attractor without the use of reconstruction phase space.
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Rajagopal, Karthikeyan, Jay Prakash Singh, Anitha Karthikeyan, and Binoy Krishna Roy. "Existence of Metastable, Hyperchaos, Line of Equilibria and Self-Excited Attractors in a New Hyperjerk Oscillator." International Journal of Bifurcation and Chaos 30, no. 13 (October 2020): 2030037. http://dx.doi.org/10.1142/s0218127420300372.
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In the past few years, chaotic systems with megastability have gained more attention in research. However, megastability behavior is mostly seen in chaotic systems. In this paper, a new 4D autonomous hyperjerk hyperchaotic system with megastability is reported.The new system has two modes of operation. The first mode considers one of its parameters [Formula: see text] and the second mode is [Formula: see text]. In the first mode, i.e. [Formula: see text] the proposed system exhibits self-excited attractors. But, in the second mode, i.e. [Formula: see text] the system has a line of equilibria. The new system has various dynamical behaviors. The chaotic nature of the proposed system is validated by circuit simulation using NI Multisim simulation software.
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Charó, Gisela D., Denisse Sciamarella, Sylvain Mangiarotti, Guillermo Artana, and Christophe Letellier. "Observability of laminar bidimensional fluid flows seen as autonomous chaotic systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 29, no. 12 (December 2019): 123126. http://dx.doi.org/10.1063/1.5120625.
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MIKOSS, I., and P. GARCÍA. "AN EXACT MAP FOR A CHAOTIC BILLIARD." International Journal of Modern Physics B 25, no. 05 (February 20, 2011): 673–81. http://dx.doi.org/10.1142/s0217979211058006.
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An exact map for Sinai's billiard with maximal central scatterer has been deduced from geometrical principles. Using this map a simple numerical method has been implemented for the search of periodic orbits. Results that seem to be useful in classical as quantum chaos are shown.
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LI, SHUJUN, GUANRONG CHEN, and XUANQIN MOU. "ON THE DYNAMICAL DEGRADATION OF DIGITAL PIECEWISE LINEAR CHAOTIC MAPS." International Journal of Bifurcation and Chaos 15, no. 10 (October 2005): 3119–51. http://dx.doi.org/10.1142/s0218127405014052.
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When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and design of chaotic pseudo-random number generators with desired characteristics.
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Martins-Filho, Luiz S., and Elbert E. N. Macau. "Patrol Mobile Robots and Chaotic Trajectories." Mathematical Problems in Engineering 2007 (2007): 1–13. http://dx.doi.org/10.1155/2007/61543.
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This paper presents a study of special trajectories attainment for mobile robots based on the dynamical features of chaotic systems. This method of trajectories construction is envisaged for missions for terrain exploration, with the specific purpose of search or patrol, where fast scanning of the robot workspace is required. We propose the imparting of chaotic motion behavior to the mobile robot by means of a planner of goal positions sequence based on an area-preserving chaotic map. As a consequence, the robot trajectories seem highly opportunistic and unpredictable for external observers, and the trajectories's characteristics ensure the quick scanning of the patrolling space. The kinematic modeling and the closed-loop control of the robot are described. The results and discussion of numerical simulations close the paper.
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Moore, R. A. "Formal quantization of a chaotic model problem." Canadian Journal of Physics 77, no. 3 (July 1, 1999): 221–33. http://dx.doi.org/10.1139/p99-020.
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A model problem, initially proposed by Feynman and Hibbs, is re-examined in this work. It is shown that the equation of motion is deterministic, in spite of its double time delay character, and has chaoticlike solutions. It is further shown that this model is amenable to the methods of higher than first-order Lagrangians, yielding a series of approximations to the initial model. Thus, for each approximation, a complete st of canonical variables can be defined, the Hamiltonian can be written down in canonical form and the conventional quantization rules applied, leading to exact quantizations. Extended sets of basis vectors follow along with the definition of physical state vectors, which are seen to contain all of the classical information. Finally, these results are used to give a possible explanation of the electron-position resonances seen in heavy-ion collision experiments that is consistent with the negative results found in low-energy electron scattering as well as other heavy-ion collision experiments.PACS Nos.: 03.20.+i, 03.65.-w, 05.45.+6
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Rather, Sajad Ahmad, and P. Shanthi Bala. "Swarm-based chaotic gravitational search algorithm for solving mechanical engineering design problems." World Journal of Engineering 17, no. 1 (February 5, 2020): 97–114. http://dx.doi.org/10.1108/wje-09-2019-0254.
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Purpose The purpose of this paper is to investigate the performance of chaotic gravitational search algorithm (CGSA) in solving mechanical engineering design frameworks including welded beam design (WBD), compression spring design (CSD) and pressure vessel design (PVD). Design/methodology/approach In this study, ten chaotic maps were combined with gravitational constant to increase the exploitation power of gravitational search algorithm (GSA). Also, CGSA has been used for maintaining the adaptive capability of gravitational constant. Furthermore, chaotic maps were used for overcoming premature convergence and stagnation in local minima problems of standard GSA. Findings The chaotic maps have shown efficient performance for WBD and PVD problems. Further, they have depicted competitive results for CSD framework. Moreover, the experimental results indicate that CGSA shows efficient performance in terms of convergence speed, cost function minimization, design variable optimization and successful constraint handling as compared to other participating algorithms. Research limitations/implications The use of chaotic maps in standard GSA is a new beginning for research in GSA particularly convergence and time complexity analysis. Moreover, CGSA can be used for solving the infinite impulsive response (IIR) parameter tuning and economic load dispatch problems in electrical sciences. Originality/value The hybridization of chaotic maps and evolutionary algorithms for solving practical engineering problems is an emerging topic in metaheuristics. In the literature, it can be seen that researchers have used some chaotic maps such as a logistic map, Gauss map and a sinusoidal map more rigorously than other maps. However, this work uses ten different chaotic maps for engineering design optimization. In addition, non-parametric statistical test, namely, Wilcoxon rank-sum test, was carried out at 5% significance level to statistically validate the simulation results. Besides, 11 state-of-the-art metaheuristic algorithms were used for comparative analysis of the experimental results to further raise the authenticity of the experimental setup.
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Shimokawa, Shinya, and Tomonori Matsuura. "Chaotic Behaviors in the Response of a Quasigeostrophic Oceanic Double Gyre to Seasonal External Forcing." Journal of Physical Oceanography 40, no. 7 (July 1, 2010): 1458–72. http://dx.doi.org/10.1175/2010jpo4400.1.
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Abstract In an oceanic double-gyre system, nonlinear oscillations of the ocean under seasonally changing external forcing are investigated using a 1.5-layer quasigeostrophic model and a simple model related to energy balance of the oceanic double gyre. In the experiments, the variable parameter is the amplitude of external seasonal forcing and the Reynolds number is fixed as 39, at which periodic shedding of inertial subgyres occurs. The authors found that entrainment (at 2 times the period of the forcing) and intermittency (on–off type), phenomena that are often seen in nonlinear systems, emerge with increasing amplitude of the forcing. They seem to be related to the generation mechanism and characteristics of long-term (from interannual to decadal) variations in the strong current region of subtropical gyres such as the Kuroshio and its extension region.
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Gao, Shengyang, Fashe Li, Qingtai Xiao, Jianxin Xu, Huage Wang, and Hua Wang. "Experimental Demonstration of Deterministic Chaos in a Waste Oil Biodiesel Semi-Industrial Furnace Combustion System." Energies 12, no. 23 (November 25, 2019): 4479. http://dx.doi.org/10.3390/en12234479.
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In this paper, the nonlinear dynamic characteristics of the oxygen-enriched combustion of waste oil biodiesel in semi-industrial furnaces were tested by the power spectrum, phase space reconstruction, the largest Lyapunov exponents, and the 0-1 test method. To express the influences of the system parameters, experiments were carried out under different oxygen content conditions (21%, 25%, 28%, 31%, and 33%). Higher oxygen enrichment degrees contribute to finer combustion sufficiency, which produces flames with high luminance. Flame luminance and temperature can be represented by different gray scale values of flame images. The chaotic characteristics of gray scale time series under different oxygen enrichment degrees were studied. With increased oxygen content, the chaotic characteristics of flame gradually developed from weak chaos to strong chaos. Furthermore, the flame maintained a stable combustion process in a high-temperature region. The stronger the chaotic characteristics of the flame, the better the combustion effect. It can be seen that the change of initial combustion conditions has a great influence on the whole combustion process. The results of several chaotic test methods were consistent. Using chaotic characteristics to analyze the waste oil biodiesel combustion process can digitize the combustion process, find the best combustion state, optimize, and precisely control it.