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Journal articles on the topic 'Chaotický systém'

Author: Grafiati

Published: 28 June 2021

Last updated: 13 February 2022

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1

SINGH, R., P. S. MOHARIR, and V. M. MARU. "COMPOUND CHAOS." International Journal of Bifurcation and Chaos 06, no. 02 (February 1996): 383–93. http://dx.doi.org/10.1142/s0218127496000138.

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Compounding is a statistical notion. Essentially, it comprises of regarding the parameters in a particular statistical distribution as random variables with a prescribed distribution. The compound distribution then acquires the parameters of the compounding distribution as its own. As deterministic chaos, in spite of being deterministic, appears like a statistical phenomenon, the notion of compounding can be extended to chaotic systems. It is shown with illustrations that a chaotic system can be compounded by another chaotic system, giving rise to compound chaos which is, in general, “chaoticer”. The concept can also be used to make a periodic system chaotic, thus opening possibilities of “chaoticization”. Examples of compound chaos and chaoticization are given using Lorenz and Rössler systems, including their attractors and limit cycles as “compoundee” and/or “compounder” systems. The conclusions are based on quantitative studies of Lyapunov exponents and correlation dimensions.

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Sun, Yeong-Jeu. "Exponential State Observer Design for a Class of Uncertain Chaotic and Non-Chaotic Systems." International Journal of Trend in Scientific Research and Development Volume-3, Issue-1 (December 31, 2018): 1158–61. http://dx.doi.org/10.31142/ijtsrd20219.

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Sun, Yeong-Jeu. "Simple Exponential Observer Design for the Generalized Liu Chaotic System." International Journal of Trend in Scientific Research and Development Volume-2, Issue-1 (December 31, 2017): 953–56. http://dx.doi.org/10.31142/ijtsrd7126.

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Sun, Yeong-Jeu, and Jer-Guang Hsieh. "Chaos Suppression and Stabilization of Generalized Liu Chaotic Control System." International Journal of Trend in Scientific Research and Development Volume-3, Issue-1 (December 31, 2018): 1112–15. http://dx.doi.org/10.31142/ijtsrd20195.

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5

Gao, Xiang, Juhyeon Lee, and Hyung-Kun Park. "Chaotic Prediction Based Channel Sensing in CR System." Transactions of The Korean Institute of Electrical Engineers 62, no. 1 (January 1, 2013): 140–42. http://dx.doi.org/10.5370/kiee.2012.62.1.140.

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Kuznetsov, S. P., V. P. Kruglov, and Y. V. Sedova. "Mechanical Systems with Hyperbolic Chaotic Attractors Based on Froude Pendulums." Nelineinaya Dinamika 16, no. 1 (2020): 51–58. http://dx.doi.org/10.20537/nd200105.

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Ma, Yancheng, Guoan Wu, and Lan Jiang. "Generalized Function Projective Lag Synchronization in Fractional-Order Chaotic Systems." International Journal of Information and Electronics Engineering 6, no. 5 (2016): 299–303. http://dx.doi.org/10.18178/ijiee.2016.6.5.642.

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Mengfan Cheng, Mengfan Cheng, and Hanping Hu Hanping Hu. "Theoretical investigations of impulsive synchronization on semiconductor laser chaotic systems." Chinese Optics Letters 10, no. 10 (2012): 101901–4. http://dx.doi.org/10.3788/col201210.101901.

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Dr.B., Gopinath, Kalyanasundaram M., Pradeepa M., and Karthika V. "Locating Hybrid Power Flow Controller in a 30-Bus System Using Chaotic Evolutionary Algorithm to Improve Power System Stability." Bonfring International Journal of Software Engineering and Soft Computing 8, no. 1 (March 30, 2018): 12–16. http://dx.doi.org/10.9756/bijsesc.8382.

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LÜ, JINHU, GUANRONG CHEN, and DAIZHAN CHENG. "A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM." International Journal of Bifurcation and Chaos 14, no. 05 (May 2004): 1507–37. http://dx.doi.org/10.1142/s021812740401014x.

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This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-scroll chaotic attractor or confine two attractors to a 2-scroll chaotic attractor under the control of a simple constant input. Furthermore, the concept of generalized Lorenz system is extended to a new class of generalized Lorenz-like systems in a canonical form. Finally, the important problems of classification and normal form of three-dimensional quadratic autonomous chaotic systems are formulated and discussed.

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Qi, Aixue, Lei Ding, and Wenbo Liu. "A Meminductor-based Chaotic System." Information Technology And Control 49, no. 2 (June 16, 2020): 317–32. http://dx.doi.org/10.5755/j01.itc.49.2.24072.

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We propose a meminductor-based chaotic system. Theoretical analysis and numerical simulations reveal complex dynamical behaviors of the proposed meminductor-based chaotic system with five unstable equilibrium points and three different states of chaotic attractors in its phase trajectory with only a single change in circuit parameter. Lyapunov exponents, bifurcation diagrams, and phase portraits are used to investigate its complex chaotic and multi-stability behaviors, including its coexisting chaotic, periodic and point attractors. The proposed meminductor-based chaotic system was implemented using analog integrators, inverters, summers, and multipliers. PSPICE simulation results verified different chaotic characteristics of the proposed circuit with a single change in a resistor value.

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12

Neunhäuserer, J. "Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems." Mathematica Bohemica 135, no. 3 (2010): 279–89. http://dx.doi.org/10.21136/mb.2010.140704.

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Wang, Lidong, Heng Liu, and Yuelin Gao. "Chaos for Discrete Dynamical System." Journal of Applied Mathematics 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/212036.

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We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.

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Bula, Inese, and Irita Rumbeniece. "CONSTRUCTION OF CHAOTIC DYNAMICAL SYSTEM." Mathematical Modelling and Analysis 15, no. 1 (February 15, 2010): 1–8. http://dx.doi.org/10.3846/1392-6292.2010.15.1-8.

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The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic.

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Gao, Y., J. W. Fan, N. Zhao, and H. Y. Yuan. "Synchronous Control of Hyper-Chaotic System Based on Inverse-System Design." Advanced Materials Research 631-632 (January 2013): 1226–30. http://dx.doi.org/10.4028/www.scientific.net/amr.631-632.1226.

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Hyper-chaotic synchronization can be applied in vast areas of physics and engineering science, and especially in secure communication. A hyper-chaotic synchronization method based on inverse-system theory is studied. The reversibility and relative degree of the synchronization error function are determined through Lie derivation calculation. A close-loop controller is obtained by synthesizing and designing a pseudo-linear feedback system, which used for estimating output variable synchronization error. Hype-chaotic synchronization of a four dimensional oscillatory system is selected as typical example and the simulation results demonstrate the validity of the method. The research results provide a useful reference for realizing hyper-chaotic synchronization.

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Wang, Xiaomin, Wenfang Zhang, Wei Guo, and Jiashu Zhang. "Secure chaotic system with application to chaotic ciphers." Information Sciences 221 (February 2013): 555–70. http://dx.doi.org/10.1016/j.ins.2012.09.037.

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17

Kal’yanov, Er V. "Controlled chaotic autooscillatory system." Technical Physics Letters 32, no. 3 (March 2006): 246–48. http://dx.doi.org/10.1134/s1063785006030217.

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Singer, J., Y.-Z. Wang, and Haim H. Bau. "Controlling a chaotic system." Physical Review Letters 66, no. 9 (March 4, 1991): 1123–25. http://dx.doi.org/10.1103/physrevlett.66.1123.

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Dalkiran, Fatma Yildirim, and J. C. Sprott. "Simple Chaotic Hyperjerk System." International Journal of Bifurcation and Chaos 26, no. 11 (October 2016): 1650189. http://dx.doi.org/10.1142/s0218127416501893.

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In literature many chaotic systems, based on third-order jerk equations with different nonlinear functions, are available. A jerk system is taken to be a part of dynamical systems that can exhibit regular and chaotic behavior. By extension, a hyperjerk system can be described as a dynamical system with [Formula: see text]th-order ordinary differential equations where [Formula: see text] is 4 or up to. Hyperjerk systems have been investigated in literature in the last decade. This paper consists of numerical studies and experimental realization on FPAA for fourth-order hyperjerk system with exponential nonlinear function.

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Sun, Junwei, Gaoyong Han, Yanfeng Wang, Hao Zhang, and Lei Wu. "Hybrid Memristor Chaotic System." Journal of Nanoelectronics and Optoelectronics 13, no. 6 (June 1, 2018): 812–18. http://dx.doi.org/10.1166/jno.2018.2326.

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21

Qi, Guoyuan, and Guanrong Chen. "A spherical chaotic system." Nonlinear Dynamics 81, no. 3 (April 23, 2015): 1381–92. http://dx.doi.org/10.1007/s11071-015-2075-4.

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22

Nepomuceno, Erivelton G., Arthur M. Lima, Janier Arias-García, Matjaž Perc, and Robert Repnik. "Minimal digital chaotic system." Chaos, Solitons & Fractals 120 (March 2019): 62–66. http://dx.doi.org/10.1016/j.chaos.2019.01.019.

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23

Yao, Yuangen, and Jun Ma. "Logical Chaotic Resonance in a Bistable System." International Journal of Bifurcation and Chaos 30, no. 13 (October 2020): 2050196. http://dx.doi.org/10.1142/s0218127420501965.

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In this work, we demonstrate a new chaotic signal-induced phenomenon that the output of a chaotic signal-driven bistable system can be consistently mapped to specific logic gate operation in an optimal window of chaotic signal intensity. We term this phenomenon logical chaotic resonance (LCR). Then, an intuitive interpretation for LCR phenomenon is given based on potential well map and mean first-passage time. Through LCR mechanism, the chaotic signal with proper intensity is used to obtain reliable logical gate in the bistable system. Besides, appropriately increasing the chaotic signal intensity can effectively improve the response speed of the bistable system to the change of input signal. Finally, the role of chaotic signal in enhancing the capacity of resisting disturbance of parameters is demonstrated.

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Li, Wangshu, Chuanfu Wang, Kai Feng, Xin Huang, and Qun Ding. "A multidimensional discrete digital chaotic encryption system." International Journal of Distributed Sensor Networks 14, no. 9 (September 2018): 155014771880278. http://dx.doi.org/10.1177/1550147718802781.

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In this article, a new multidimensional discrete chaotic system is proposed, and the characteristics and advantages of the multidimensional discrete chaotic system are analyzed. The multidimensional discrete chaotic system is designed using digital technology, and the system has the complexity of hyper-chaotic system, and it can avoid the choice of step size, at the same time, the design of the circuit is simple, the resource occupancy rate is low, it is suitable for the design of digital system, and so on. It can be used in constructing chaotic sequence generator, chaotic encryption, and visual sensor networks.

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Wu, Xian Yong, Yi Long Cheng, Kai Liu, Xin Liang Yu, and Xian Qian Wu. "Chaos Synchronization between Fractional-Order Unified Chaotic System and Rossler Chaotic System." Advanced Materials Research 562-564 (August 2012): 2088–91. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.2088.

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The chaotic dynamics of the unified chaotic system and the Rossler system with different fractional-order are studied in this paper. The research shows that the chaotic attractors can be found in the two systems while the orders of the systems are less than three. Asymptotic synchronization of response and drive systems is realized by active control through designing proper controller when system parameters are known. Theoretical analysis and simulation results demonstrate the effective of this method.

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Zhou Ping and Kuang Fei. "Synchronization between fractional-order chaotic system and chaotic system of integer orders." Acta Physica Sinica 59, no. 10 (2010): 6851. http://dx.doi.org/10.7498/aps.59.6851.

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27

Yin, Tao, and Yiming Wang. "Nonlinear analysis and prediction of soybean futures." Agricultural Economics (Zemědělská ekonomika) 67, No. 5 (May 20, 2021): 200–207. http://dx.doi.org/10.17221/480/2020-agricecon.

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We use chaotic artificial neural network (CANN) technology to predict the price of the most widely traded agricultural futures – soybean futures. The nonlinear existence test results show that the time series of soybean futures have multifractal dynamics, long-range dependence, self similarity, and chaos characteristics. This also provides a basis for the construction of a CANN model. Compared with the artificial neural network (ANN) structure as our benchmark system, the predictability of CANN is much higher. The ANN is based on Gaussian kernel function and is only suitable for local approximation of nonstationary signals, so it cannot approach the global nonlinear chaotical hidden pattern. Improving the prediction accuracy of soybean futures prices is of great significance for investors, soybean producers, and decision makers.

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Lai, Qiang, and Shiming Chen. "Generating Multiple Chaotic Attractors from Sprott B System." International Journal of Bifurcation and Chaos 26, no. 11 (October 2016): 1650177. http://dx.doi.org/10.1142/s0218127416501777.

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Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear phenomenon, but there are few studies that have previously addressed it to our best knowledge. In this paper, we propose a polynomial function method for generating multiple chaotic attractors from the Sprott B system. The polynomial function extends the number of index-2 saddle foci, which determines the emergence of multiple chaotic attractors in the system. The analysis of the equilibria is presented. Two coexisting chaotic attractors, three coexisting chaotic attractors and four coexisting chaotic attractors are investigated for verifying the effectiveness of the method. The chaotic characteristics of the attractors are shown by bifurcation diagrams, Lyapunov exponent spectrum and phase portraits.

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Pham, Viet-Thanh, Sajad Jafari, Xiong Wang, and Jun Ma. "A Chaotic System with Different Shapes of Equilibria." International Journal of Bifurcation and Chaos 26, no. 04 (April 2016): 1650069. http://dx.doi.org/10.1142/s0218127416500693.

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Although many chaotic systems have been introduced in the literature, a few of them possess uncountably infinite equilibrium points. The aim of our short work is to widen the current knowledge of the chaotic systems with an infinite number of equilibria. A three-dimensional system with special properties, for example, exhibiting chaotic attractor with circular equilibrium, chaotic attractor with ellipse equilibrium, chaotic attractor with square-shaped equilibrium, and chaotic attractor with rectangle-shaped equilibrium, is proposed.

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Qi, Guoyuan, and Xiyin Liang. "Force Analysis of Qi Chaotic System." International Journal of Bifurcation and Chaos 26, no. 14 (December 30, 2016): 1650237. http://dx.doi.org/10.1142/s0218127416502370.

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The Qi chaotic system is transformed into Kolmogorov type of system. The vector field of the Qi chaotic system is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. Angular momentum representing the physical analogue of the state variables of the chaotic system is identified. The Casimir energy law relating to the orbital behavior is identified and the bound of Qi chaotic attractor is given. Five cases of study have been conducted to discover the insights and functions of different types of torques of the chaotic attractor and also the key factors of producing different types of modes of dynamics.

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Jeong, Jae-Ho, Goo-Man Park, Tae-Hyun Jeon, Bo-Seok Seo, Kyung-Sup Kwak, Yeong-Min Jang, Sang-Yule Choi, and Jae-Sang Cha. "A study of mitigated interference Chaotic-OOK system in IEEE802.15.4a." Journal of Broadcast Engineering 12, no. 2 (March 29, 2007): 148–58. http://dx.doi.org/10.5909/jbe.2007.12.2.148.

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Zhu, Jian Liang, and Chun Yu Yu. "Seven Dimension Chaotic System and its Circuit Implementation." Advanced Materials Research 588-589 (November 2012): 1251–54. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.1251.

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In order to generate more complex chaotic attractors, a seven-dimensional chaotic system is constructed, and relevant chaotic attractors can be obtained by Matlab numerical simulation. Lyapunov exponents validate that the system is chaotic. Implementation circuit of this system is designed, and circuit simulation can be done by using Multisim. Circuit simulation result is identical to system simulation completely. Chaotic behavior of the system is proved farther. A new chaotic signal source is provided for practical application based on chaos such as secrecy communication and signal encryption fields.

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YANG, TAO, and LEON O. CHUA. "CHAOTIC IMPULSE RADIO: A NOVEL CHAOTIC SECURE COMMUNICATION SYSTEM." International Journal of Bifurcation and Chaos 10, no. 02 (February 2000): 345–57. http://dx.doi.org/10.1142/s0218127400000220.

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A chaotic impulse radio system is an ultrawide-band communication system that uses a train of very narrow baseband impulses as a carrier. In the transmitter of a chaotic impulse radio system, a message signal is modulated by two kinds of pulse carriers. Firstly, a frequency modulation is used to modulate the message signal into a subcarrier that functions as the clock pulses of a chaotic circuit. Driven by the modulated clock pulses, the chaotic circuit outputs a chaotic impulse positioning sequence which generates the positions of the carrier impulses. The specially designed chaotic circuit in the transmitter guarantees that the time intervals between the carrier impulses are chaotic. Thus the energy of the impulse carrier is distributed evenly over the entire bandwidth. In the receiver of a chaotic impulse radio system the message signal is demodulated in two stages. At the first stage, the time interval between two consecutive impulses is recovered. At the second stage, a simple algorithm based on the knowledge of the chaotic circuit in the transmitter is used to calculate partially the locations of the inner clock pulses which in turn are used to demodulate the message signal. No synchronization at any level is needed in this chaotic impulse radio system. The security of this chaotic impulse radio system depends on the hardware parameters of the chaotic circuit and the inner clock pulse train. Simulation results are presented to illustrate the design procedure of an example of this chaotic impulse radio system.

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Gang, Zhang, Li Fang He, and Tian Qi Zhang. "A Image Transmission System Based on Logistic Map." Advanced Materials Research 468-471 (February 2012): 727–32. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.727.

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A method for chaotic synchronization system based on nonlinear control was studied. The general approach to chaotic system is following Logistic map. First, the parameter which meets chaotic status was analyzed and found via bifurcation diagram and Lyapunov exponent spectrum. The system can be synchronized quickly after just only a single iteration. Then, the method of implementing the synchronization system within a chaotic parameter modulation based communication system was researched. The deduction and simulation results also showed the probability for implementation the system in fast secure chaotic communications that require instant synchronization schemes. Finally, the chaotic system was applied in image transmission and the simulation results were also given.

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KANSO, ALI. "CONTROLLED HENON SYSTEM AND ITS CRYPTOGRAPHIC APPLICATIONS." International Journal of Bifurcation and Chaos 20, no. 08 (August 2010): 2487–506. http://dx.doi.org/10.1142/s021812741002712x.

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This paper proposes a modification of the controlled chaotic Henon system suggested in [Li et al., 2004]. The dynamics of the proposed and existing 2-D systems are analyzed and new chaotic attractors are found in them. We show that these systems exhibit chaotic behavior for a wide range of control parameters. We also construct a chaotic modulation scheme with feedback based on a single controlled chaotic Henon system for use in cryptographic applications. The efficiency of this communication scheme is analyzed and is shown to provide a high level of security, resulting from the proper use of controllers. Furthermore, we propose a technique for generating random-like binary digits from the suggested controlled chaotic Henon systems. Unlike binary digits generated by chaotic Henon systems which usually do not possess random-like properties, the digits generated here are shown (numerically using the NIST statistical test suite) to possess excellent random-like properties. Furthermore, the generated bit sequences are demonstrated to have a large period, which may have useful applications in cryptography.

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Wang, Luyao, and Hai Cheng. "Pseudo-Random Number Generator Based on Logistic Chaotic System." Entropy 21, no. 10 (September 30, 2019): 960. http://dx.doi.org/10.3390/e21100960.

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In recent years, a chaotic system is considered as an important pseudo-random source to pseudo-random number generators (PRNGs). This paper proposes a PRNG based on a modified logistic chaotic system. This chaotic system with fixed system parameters is convergent and its chaotic behavior is analyzed and proved. In order to improve the complexity and randomness of modified PRNGs, the chaotic system parameter denoted by floating point numbers generated by the chaotic system is confused and rearranged to increase its key space and reduce the possibility of an exhaustive attack. It is hard to speculate on the pseudo-random number by chaotic behavior because there is no statistical characteristics and infer the pseudo-random number generated by chaotic behavior. The system parameters of the next chaotic system are related to the chaotic values generated by the previous ones, which makes the PRNG generate enough results. By confusing and rearranging the output sequence, the system parameters of the previous time cannot be gotten from the next time which ensures the security. The analysis shows that the pseudo-random sequence generated by this method has perfect randomness, cryptographic properties and can pass the statistical tests.

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Zhu, Hegui, Wentao Qi, Jiangxia Ge, and Yuelin Liu. "Analyzing Devaney Chaos of a Sine–Cosine Compound Function System." International Journal of Bifurcation and Chaos 28, no. 14 (December 30, 2018): 1850176. http://dx.doi.org/10.1142/s0218127418501766.

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The one-dimensional Sine map and Chebyshev map are classical chaotic maps, which have clear chaotic characteristics. In this paper, we establish a chaotic framework based on a Sine–Cosine compound function system by analyzing the existing one-dimensional Sine map and Chebyshev map. The sensitive dependence on initial conditions, topological transitivity and periodic-point density of this chaotic framework is proved, showing that the chaotic framework satisfies Devaney’s chaos definition. In order to illustrate the chaotic behavior of the chaotic framework, we propose three examples, called Cosine–Polynomial (C–P) map, Sine–Tangent (S–T) map and Sine–Exponent (S–E) map, respectively. Then, we evaluate the chaotic behavior with Sine map and Chebyshev map by analyzing bifurcation diagrams, Lyapunov exponents, correlation dimensions, Kolmogorov entropy and [Formula: see text] complexity. Experimental results show that the chaotic framework has better unpredictability and more complex chaotic behaviors than the classical Sine map and Chebyshev map. The results also verify the effectiveness of the theoretical analysis of the proposed chaotic framework.

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Wu, Hao, Bo Lun Xu, Chang Fan, and Xian Yong Wu. "Chaos Synchronization Between Unified Chaotic System And Rossler System." Applied Mechanics and Materials 321-324 (June 2013): 2464–70. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2464.

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In this paper, two synchronization schemes between two different chaotic systems are proposed. Chaos synchronization between unified chaotic system and Rossler system via active control and adaptive control are investigated. Different controllers are designed to synchronize the drive and response systems. Active control synchronization is used when system parameters are known; adaptive synchronization is employed when system parameters are unknown or uncertain. Simulation results show the effectiveness of the proposed schemes.

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Wu, Xian Yong, Hao Wu, and Hao Gong. "Chaos Anti-Synchronization between Chen System and Lu System." Applied Mechanics and Materials 631-632 (September 2014): 710–13. http://dx.doi.org/10.4028/www.scientific.net/amm.631-632.710.

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Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

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Xiong, Li, Zhenlai Liu, and Xinguo Zhang. "Analysis, circuit implementation and applications of a novel chaotic system." Circuit World 43, no. 3 (August 7, 2017): 118–30. http://dx.doi.org/10.1108/cw-02-2017-0007.

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Purpose Lack of optimization and improvement on experimental circuits precludes comprehensive statements. It is a deficiency of the existing chaotic circuit technology. One of the aims of this paper is to solve the above mentioned problems. Another purpose of this paper is to construct a 10 + 4-type chaotic secure communication circuit based on the proposed third-order 4 + 2-type circuit which can output chaotic phase portraits with high accuracy and high stability. Design/methodology/approach In Section 2 of this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new third-order Lorenz-like chaotic system is proposed based on the 4 + 2 circuit. Then some simulations are presented to verify that the proposed system is chaotic by using Multisim software. In Section 3, a fourth-order chaotic circuit is proposed on the basis of the third-order 4 + 2 chaotic circuit. In Section 4, the circuit design method of this paper is applied to chaotic synchronization and secure communication. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. In Section 5, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented in an analog electronic circuit. The analog circuit implementation results match the Multisim results. Findings The simulation results show that the proposed fourth-order chaotic circuit can output six phase portraits, and it can output a stable fourth-order double-vortex chaotic signal. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. The scheme has the advantages of clear thinking, efficient and high practicability. The experimental results show that the precision is improved by 2-3 orders of magnitude. Signal-to-noise ratio meets the requirements of engineering design. It provides certain theoretical and technical bases for the realization of a large-scale integrated circuit with a memristor. The proposed circuit design method can also be used in other chaotic systems. Originality/value In this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new chaotic system is proposed on the basis of the 4 + 2 chaotic circuit for the first time. Some simulations are presented to verify its chaotic characteristics by Multisim. Then the novel third-order 4 + 2 chaotic circuit is applied to construct a fourth-order chaotic circuit. Simulation results verify the existence of the new fourth-order chaotic system. Moreover, a new 10 + 4-type chaotic secure communication circuit is proposed based on chaotic synchronization of the novel third-order 4 + 2 circuit. To illustrate the effectiveness of the proposed scheme, the intensity limit and stability of the transmitted signal, the characteristic of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. Finally, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented through an analog electronic circuit, which are characterized by their high accuracy and good robustness. The analog circuit implementation results match the Multisim results.

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Du, Jian-Rong, Chun-Lai Li, Kun Qian, Zhao-Yu Li, and Wen Li. "Study on Amplitude Modulation Principle of Chaotic System." Complexity 2020 (February 11, 2020): 1–13. http://dx.doi.org/10.1155/2020/9106132.

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Exploring the amplitude modulation phenomenon of chaotic signal has become a subject of great concern in recent years. This paper mainly concentrates on the preliminary study on amplitude modulation principle of a chaotic system. First, two 3D chaotic systems with quadratic product terms are introduced for studying the amplitude modulation phenomenon of chaotic signal. It is found that the signal amplitude of the first system can be controlled by partial quadratic coefficient. But for the second system, none of nonlinear coefficient can be employed to control the signal amplitude. Then, the amplitude modulation principle of chaotic system is preliminarily studied by exploring the intrinsic relationship between nonzero equilibrium point and phase space trajectory, and it is further validated by introducing unified parameter to the two 3D chaotic systems. As a necessary condition, the principle provides a feasible and simple method for constructing and analyzing an amplitude modulation chaotic system.

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LI, CHUNLAI, SIMIN YU, and XIAOSHU LUO. "A RING-SCROLL CHUA SYSTEM." International Journal of Bifurcation and Chaos 23, no. 10 (October 2013): 1350170. http://dx.doi.org/10.1142/s0218127413501708.

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In this paper, we propose a ring-scroll Chua system by introducing a generalized ring transformation. Some basic dynamical properties of this generalized ring transformation are discussed. The parameter regions and the periodic orbits, which are embedded in Chua chaotic attractor mapping to those in ring-scroll Chua chaotic attractor, are investigated, too. Moreover, the topological horseshoe of this system is investigated. Finally, the ring-scroll Chua chaotic attractor is physically implemented by using digital signal processors.

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Kacar, Sezgin, Zhouchao Wei, Akif Akgul, and Burak Aricioglu. "A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System." Zeitschrift für Naturforschung A 73, no. 7 (July 26, 2018): 595–607. http://dx.doi.org/10.1515/zna-2018-0030.

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AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

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Yan, Jian-ping, and Chang-pin Li. "Generalized projective synchronization for the chaotic Lorenz system and the chaotic Chen system." Journal of Shanghai University (English Edition) 10, no. 4 (August 2006): 299–304. http://dx.doi.org/10.1007/s11741-006-0004-y.

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Zhu, Jian Liang, Yu Jing Wang, and Shou Qiang Kang. "Six-Dimensional Chaotic System and its Circuit Implementation." Advanced Materials Research 255-260 (May 2011): 2018–22. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.2018.

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In order to generate complex chaotic attractors, a six-dimensional chaotic system is designed, which contains six parameters and each equation contains a nonlinear product term. When its parameters satisfy certain conditions, the system is chaotic. By Matlab numerical simulation, chaotic attractor and relevant Lyapunov exponents spectrum can be obtained, which validates that the system is chaotic. And, time domain waveform and power spectrum are shown. Finally, the implementation circuit of this system is designed, and circuit simulation can be done by using Multisim. Circuit simulation result is identical to system simulation completely. The circuit has a practical significance in secrecy communication and correlative fields.

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Singh, Jay Prakash, Pankaj Prakash, Karthikeyan Rajagopal, Riessom Weldegiorgis, Prakash Duraisamy, and Binoy Krishna Roy. "Bifurcation and chaos in a bearing system." International Journal of Modern Physics B 34, no. 19 (July 28, 2020): 2050176. http://dx.doi.org/10.1142/s0217979220501763.

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In this paper, the chaotic phenomenon is reported in a bearing system. The chaotic dynamics of the new system is first derived from an available bearing system. The proposed system is then analyzed using various tools to observe its dynamical behaviors. Theoretical and simulation results confirm the presence of chaotic and periodic behaviors in the new bearing system.

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Voliansky, Roman. "Transformation of the generalized chaotic system into canonical form." International Journal of Advances in Intelligent Informatics 3, no. 3 (December 1, 2017): 117. http://dx.doi.org/10.26555/ijain.v3i3.113.

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The paper deals with the developing of the numerical algorithms for transformation of generalized chaotic system into canonical form. Such transformation allows us to simplify control algorithm for chaotic system. These algorithms are defined by using Lie derivatives for output variable and solution of nonlinear equations. Usage of proposed algorithm is one of the ways for discovering of new chaotic attractors. These attractors can be obtained by transformation of known chaotic systems into various state spaces. Transformed attractors depend on both parameters of chaotic system and sample time of its discrete model.

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Wei, Peng Cheng, Wei Ran, and Jun Jian Huang. "A Novel Secure Communication Scheme Based on Chaotic System." Advanced Materials Research 255-260 (May 2011): 2242–47. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.2242.

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A secure communication scheme based on piecewise linear chaotic system is proposed. Two Chaotic Systems are used in this algorithm, with a symbolic sequence generated by a Chaotic System the message sequence is tracked, employing the chaotic masking technique the message for transmitted is encrypted with a binary sequence extracted from another Chaotic System. The theoretic and experience results stated that the proposed algorithm has many properties such as high speed and easy implementing and high security and it is suitable for practical use in the secure communication.

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LÜ, JINHU, GUANRONG CHEN, DAIZHAN CHENG, and SERGEJ CELIKOVSKY. "BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM." International Journal of Bifurcation and Chaos 12, no. 12 (December 2002): 2917–26. http://dx.doi.org/10.1142/s021812740200631x.

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This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

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Sambas, Aceng, Mustafa Mamat, Sundarapandian Vaidyanathan, Muhammad Mohamed, and Mada Sanjaya. "A New 4-D Chaotic System with Hidden Attractor and its Circuit Implementation." International Journal of Engineering & Technology 7, no. 3 (June 30, 2018): 1245. http://dx.doi.org/10.14419/ijet.v7i3.9846.

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In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.

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