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Publié le 22 juillet 2024

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1

Chandrasekaran, Jeyamala, et S. J. Thiruvengadam. « Ensemble of Chaotic and Naive Approaches for Performance Enhancement in Video Encryption ». Scientific World Journal 2015 (2015) : 1–11. http://dx.doi.org/10.1155/2015/458272.

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Owing to the growth of high performance network technologies, multimedia applications over the Internet are increasing exponentially. Applications like video conferencing, video-on-demand, and pay-per-view depend upon encryption algorithms for providing confidentiality. Video communication is characterized by distinct features such as large volume, high redundancy between adjacent frames, video codec compliance, syntax compliance, and application specific requirements. Naive approaches for video encryption encrypt the entire video stream with conventional text based cryptographic algorithms. Although naive approaches are the most secure for video encryption, the computational cost associated with them is very high. This research work aims at enhancing the speed of naive approaches through chaos based S-box design. Chaotic equations are popularly known for randomness, extreme sensitivity to initial conditions, and ergodicity. The proposed methodology employs two-dimensional discrete Henon map for (i) generation of dynamic and key-dependent S-box that could be integrated with symmetric algorithms like Blowfish and Data Encryption Standard (DES) and (ii) generation of one-time keys for simple substitution ciphers. The proposed design is tested for randomness, nonlinearity, avalanche effect, bit independence criterion, and key sensitivity. Experimental results confirm that chaos based S-box design and key generation significantly reduce the computational cost of video encryption with no compromise in security.

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2

CONNELL, BENJAMIN S. H., et DICK K. P. YUE. « Flapping dynamics of a flag in a uniform stream ». Journal of Fluid Mechanics 581 (22 mai 2007) : 33–67. http://dx.doi.org/10.1017/s0022112007005307.

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We consider the flapping stability and response of a thin two-dimensional flag of high extensional rigidity and low bending rigidity. The three relevant non-dimensional parameters governing the problem are the structure-to-fluid mass ratio, μ = ρsh/(ρfL); the Reynolds number, Rey = VL/ν; and the non-dimensional bending rigidity, KB = EI/(ρfV2L3). The soft cloth of a flag is represented by very low bending rigidity and the subsequent dominance of flow-induced tension as the main structural restoring force. We first perform linear analysis to help understand the relevant mechanisms of the problem and guide the computational investigation. To study the nonlinear stability and response, we develop a fluid–structure direct simulation (FSDS) capability, coupling a direct numerical simulation of the Navier–Stokes equations to a solver for thin-membrane dynamics of arbitrarily large motion. With the flow grid fitted to the structural boundary, external forcing to the structure is calculated from the boundary fluid dynamics. Using a systematic series of FSDS runs, we pursue a detailed analysis of the response as a function of mass ratio for the case of very low bending rigidity (KB = 10−4) and relatively high Reynolds number (Rey = 103). We discover three distinct regimes of response as a function of mass ratio μ: (I) a small μ regime of fixed-point stability; (II) an intermediate μ regime of period-one limit-cycle flapping with amplitude increasing with increasing μ; and (III) a large μ regime of chaotic flapping. Parametric stability dependencies predicted by the linear analysis are confirmed by the nonlinear FSDS, and hysteresis in stability is explained with a nonlinear softening spring model. The chaotic flapping response shows up as a breaking of the limit cycle by inclusion of the 3/2 superharmonic. This occurs as the increased flapping amplitude yields a flapping Strouhal number (St = 2Af/V) in the neighbourhood of the natural vortex wake Strouhal number, St ≃ 0.2. The limit-cycle von Kármán vortex wake transitions in chaos to a wake with clusters of higher intensity vortices. For the largest mass ratios, strong vortex pairs are distributed away from the wake centreline during intermittent violent snapping events, characterized by rapid changes in tension and dynamic buckling.

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Zotos, Euaggelos E., et F. L. Dubeibe. « Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system ». International Journal of Modern Physics D 27, n^o 04 (mars 2018) : 1850036. http://dx.doi.org/10.1142/s0218271818500360.

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The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g. a comet, asteroid, meteor or spacecraft) in the planar Sun–Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with the earlier ones regarding other planetary systems.

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Liu, Juan, Xiang Zhang, Jian Yang, Junhui Zhou, Yuan Yuan, Chao Jiang, Xiulian Chi et Luqi Huang. « Agarwood wound locations provide insight into the association between fungal diversity and volatile compounds in Aquilaria sinensis ». Royal Society Open Science 6, n^o 7 (juillet 2019) : 190211. http://dx.doi.org/10.1098/rsos.190211.

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The aim of the present study was to investigate the effect of wound location on the fungal communities and volatile distribution of agarwood in Aquilaria sinensis . Two-dimensional gas chromatography with high-resolution time-of-flight mass spectrometry revealed 60 compounds from the NIST library, including 25 sesquiterpenes, seven monoterpenes, two diterpenes, nine aromatics, nine alkanes and eight others. Of five agarwood types, Types IV and II contained the greatest number and concentration of sesquiterpenes, respectively. The fungal communities of the agarwood were dominated by the phylum Ascomycota and were significantly affected by the type of wound tissue. Community richness indices (observed species, Chao1, PD whole tree, ACE indices) indicated that Types I and IV harboured the most and least species-rich fungal communities, and the fungal communities of Types V, I, III and IV/II were dominated by Lasiodiplodia , Hydnellum , Phaeoisaria and Ophiocordyceps species, respectively. Correlations between fungal species and agarwood components revealed that the chemical properties of A. sinensis were associated with fungal diversity. More specifically, the dominant fungal genera of Types V, I and III ( Lasiodiplodia , Hydnellum and Phaeoisaria , respectively) were strongly correlated with specific terpenoid compounds. The finding that wound location affects the fungal communities and volatile distribution of agarwood provides insight into the formation of distinct agarwood types.

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Harrison, Mary Ann, et Ying-Cheng Lai. « Route to high-dimensional chaos ». Physical Review E 59, n^o 4 (1 avril 1999) : R3799—R3802. http://dx.doi.org/10.1103/physreve.59.r3799.

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HARRISON, MARY ANN, et YING-CHENG LAI. « BIFURCATION TO HIGH-DIMENSIONAL CHAOS ». International Journal of Bifurcation and Chaos 10, n^o 06 (juin 2000) : 1471–83. http://dx.doi.org/10.1142/s0218127400000967.

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High-dimensional chaos has been an area of growing recent investigation. The questions of how dynamical systems become high-dimensionally chaotic with multiple positive Lyapunov exponents, and what the characteristic features associated with the transition are, remain less investigated. In this paper, we present one possible route to high-dimensional chaos. By this route, a subsystem becomes chaotic with one positive Lyapunov exponent via one of the known routes to low-dimensional chaos, after which the complementary subsystem becomes chaotic, leading to additional positive Lyapunov exponents for the whole system. A characteristic feature of this route is that the additional Lyapunov exponents pass through zero smoothly. As a consequence, the fractal dimension of the chaotic attractor changes continuously through the transition, in contrast to the transition to low-dimensional chaos at which the fractal dimension changes abruptly. We present a heuristic theory and numerical examples to illustrate this route to high-dimensional chaos.

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Saiki, Yoshitaka, Miguel A. F. Sanjuán et James A. Yorke. « Low-dimensional paradigms for high-dimensional hetero-chaos ». Chaos : An Interdisciplinary Journal of Nonlinear Science 28, n^o 10 (octobre 2018) : 103110. http://dx.doi.org/10.1063/1.5045693.

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Auerbach, Ditza, Celso Grebogi, Edward Ott et James A. Yorke. « Controlling chaos in high dimensional systems ». Physical Review Letters 69, n^o 24 (14 décembre 1992) : 3479–82. http://dx.doi.org/10.1103/physrevlett.69.3479.

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Blokhina, Elena V., Sergey P. Kuznetsov et Andrey G. Rozhnev. « High-Dimensional Chaos in a Gyrotron ». IEEE Transactions on Electron Devices 54, n^o 2 (février 2007) : 188–93. http://dx.doi.org/10.1109/ted.2006.888757.

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MUSIELAK, Z. E., et D. E. MUSIELAK. « HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS ». International Journal of Bifurcation and Chaos 19, n^o 09 (septembre 2009) : 2823–69. http://dx.doi.org/10.1142/s0218127409024517.

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Studies of nonlinear dynamical systems with many degrees of freedom show that the behavior of these systems is significantly different as compared with the behavior of systems with less than two degrees of freedom. These findings motivated us to carry out a survey of research focusing on the behavior of high-dimensional chaos, which include onset of chaos, routes to chaos and the persistence of chaos. This paper reports on various methods of generating and investigating nonlinear, dissipative and driven dynamical systems that exhibit high-dimensional chaos, and reviews recent results in this new field of research. We study high-dimensional Lorenz, Duffing, Rössler and Van der Pol oscillators, modified canonical Chua's circuits, and other dynamical systems and maps, and we formulate general rules of high-dimensional chaos. Basic techniques of chaos control and synchronization developed for high-dimensional dynamical systems are also reviewed.

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Hu, Gang, Ying Zhang, Hilda A. Cerdeira et Shigang Chen. « From Low-Dimensional Synchronous Chaos to High-Dimensional Desynchronous Spatiotemporal Chaos in Coupled Systems ». Physical Review Letters 85, n^o 16 (16 octobre 2000) : 3377–80. http://dx.doi.org/10.1103/physrevlett.85.3377.

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Ding, Mingzhou. « Synchronization of chaos in high dimensional systems ». IFAC Proceedings Volumes 32, n^o 2 (juillet 1999) : 2024–28. http://dx.doi.org/10.1016/s1474-6670(17)56343-0.

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Lepri, S., G. Giacomelli, A. Politi et F. T. Arecchi. « High-dimensional chaos in delayed dynamical systems ». Physica D : Nonlinear Phenomena 70, n^o 3 (janvier 1994) : 235–49. http://dx.doi.org/10.1016/0167-2789(94)90016-7.

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Sasa, S. i., et T. S. Komatsu. « Thermodynamic Irreversibility from High-Dimensional Hamiltonian Chaos ». Progress of Theoretical Physics 103, n^o 1 (1 janvier 2000) : 1–52. http://dx.doi.org/10.1143/ptp.103.1.

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BROWN, RAY, ROBERT BEREZDIVIN et LEON O. CHUA. « CHAOS AND COMPLEXITY ». International Journal of Bifurcation and Chaos 11, n^o 01 (janvier 2001) : 19–26. http://dx.doi.org/10.1142/s0218127401001992.

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In this paper we show how to relate a form of high-dimensional complexity to chaotic and other types of dynamical systems. The derivation shows how "near-chaotic" complexity can arise without the presence of homoclinic tangles or positive Lyapunov exponents. The relationship we derive follows from the observation that the elements of invariant finite integer lattices of high-dimensional dynamical systems can, themselves, be viewed as single integers rather than coordinates of a point in n-space. From this observation it is possible to construct high-dimensional dynamical systems which have properties of shifts but for which there is no conventional topological conjugacy to a shift. The particular manner in which the shift appears in high-dimensional dynamical systems suggests that some forms of complexity arise from the presence of chaotic dynamics which are obscured by the large dimensionality of the system domain.

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Reiterer, Peter, Claudia Lainscsek, Ferdinand Schürrer, Christophe Letellier et Jean Maquet. « A nine-dimensional Lorenz system to study high-dimensional chaos ». Journal of Physics A : Mathematical and General 31, n^o 34 (28 août 1998) : 7121–39. http://dx.doi.org/10.1088/0305-4470/31/34/015.

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WENNEKERS, THOMAS, et FRANK PASEMANN. « SYNCHRONOUS CHAOS IN HIGH-DIMENSIONAL MODULAR NEURAL NETWORKS ». International Journal of Bifurcation and Chaos 06, n^o 11 (novembre 1996) : 2055–67. http://dx.doi.org/10.1142/s0218127496001338.

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The relationship between certain types of high-dimensional neural networks and low-dimensional prototypical equations (neuromodules) is investigated. The high-dimensional systems consist of finitely many pools containing identical, dissipative and nonlinear single-units operating in discrete time. Under the assumption of random connections inside and between pools, the system can be reduced to a set of only a few equations, which — asymptotically in time and system size — describe the behavior of every single unit arbitrarily well. This result can be viewed as synchronization of the single units in each pool. It is stated as a theorem on systems of nonlinear coupled maps, which gives explicit conditions on the single unit dynamics and the nature of the random connections. As an application we compare a 2-pool network with the corresponding two-dimensional dynamics. The bifurcation diagrams of both systems become very similar even for moderate system size (N=50) and large disorder in the connection strengths (50% of mean), despite the fact, that the systems exhibit fairly complex behavior (quasiperiodicity, chaos, coexisting attractors).

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Li, Qi-Xiu, et Ke-Jun Li. « Low-Dimensional Chaos of High-Latitude Solar Activity ». Publications of the Astronomical Society of Japan 59, n^o 5 (25 octobre 2007) : 983–87. http://dx.doi.org/10.1093/pasj/59.5.983.

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19

PAZÓ, DIEGO, ESTEBAN SÁNCHEZ et MANUEL A. MATÍAS. « TRANSITION TO HIGH-DIMENSIONAL CHAOS THROUGH QUASIPERIODIC MOTION ». International Journal of Bifurcation and Chaos 11, n^o 10 (octobre 2001) : 2683–88. http://dx.doi.org/10.1142/s0218127401003747.

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In this contribution we report on a transition to high-dimensional chaos through three-frequency quasiperiodic behavior. The resulting chaotic attractor has a one positive and two null Lyapunov exponents. The transition occurs at the point at which two symmetry related three-dimensional tori merge in a crisis-like bifurcation. The route can be summarized as: 2D torus → 3D torus → high-dimensional chaotic attractor.

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Mestl, Thomas, Chris Lemay et Leon Glass. « Chaos in high-dimensional neural and gene networks ». Physica D : Nonlinear Phenomena 98, n^o 1 (novembre 1996) : 33–52. http://dx.doi.org/10.1016/0167-2789(96)00086-3.

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Reynolds, Robert R., Lawrence N. Virgin et Earl H. Dowell. « High-dimensional chaos can lead to weak turbulence ». Nonlinear Dynamics 4, n^o 6 (décembre 1993) : 531–46. http://dx.doi.org/10.1007/bf00162231.

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Sosnovtseva, O., et E. Mosekilde. « Torus Destruction and Chaos–Chaos Intermittency in a Commodity Distribution Chain ». International Journal of Bifurcation and Chaos 07, n^o 06 (juin 1997) : 1225–42. http://dx.doi.org/10.1142/s0218127497000996.

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The destruction of two-dimensional tori T2 and the transitions to chaos are studied numerically in a high-dimensional model describing the decision making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the "system pursues the ghost" of a vanished hyperchaotic attractor are studied.

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Lai, Ying-Cheng, Erik M. Bollt et Zonghua Liu. « Low-dimensional chaos in high-dimensional phase space : how does it occur ? » Chaos, Solitons & ; Fractals 15, n^o 2 (janvier 2003) : 219–32. http://dx.doi.org/10.1016/s0960-0779(02)00094-2.

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Cheng, Wei, Junbo Feng, Yan Wang, Zheng Peng, Hao Cheng, Xiaodong Ren, Yubei Shuai et al. « High precision reconstruction of silicon photonics chaos with stacked CNN-LSTM neural networks ». Chaos : An Interdisciplinary Journal of Nonlinear Science 32, n^o 5 (mai 2022) : 053112. http://dx.doi.org/10.1063/5.0082993.

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Silicon-based optical chaos has many advantages, such as compatibility with complementary metal oxide semiconductor (CMOS) integration processes, ultra-small size, and high bandwidth. Generally, it is challenging to reconstruct chaos accurately because of its initial sensitivity and high complexity. Here, a stacked convolutional neural network (CNN)-long short-term memory (LSTM) neural network model is proposed to reconstruct optical chaos with high accuracy. Our network model combines the advantages of both CNN and LSTM modules. Further, a theoretical model of integrated silicon photonics micro-cavity is introduced to generate chaotic time series for use in chaotic reconstruction experiments. Accordingly, we reconstructed the one-dimensional, two-dimensional, and three-dimensional chaos. The experimental results show that our model outperforms the LSTM, gated recurrent unit (GRU), and CNN models in terms of MSE, MAE, and R-squared metrics. For example, the proposed model has the best value of this metric, with a maximum improvement of 83.29% and 49.66%. Furthermore, 1D, 2D, and 3D chaos were all significantly improved with the reconstruction tasks.

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RUFFO, STEFANO. « CHAOS IN COUPLED ROTATORS ». International Journal of Modern Physics C 04, n^o 02 (avril 1993) : 375–83. http://dx.doi.org/10.1142/s0129183193000409.

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We show that time averages of physical observables agree with ensemble averages provided chaos is present and widespread in a model system of coupled rotators. Slow relaxation is present both at low and at high temperature, where chaos is weak and inefficient. A 1.5 dimensional Hamiltonian describes the high dimensional motion quite well and allows the introduction of a Chirikov overlap parameter. A Gibbsian calculation of this parameter predicts the high temperature threshold to the statistical regime. The onset of nonlinearity is instead the mechanism which leads to the statistical regime on the low temperature side. This result should prove of interest for understanding and controlling the relaxation to equilibrium of molecular dynamics simulations. Moreover it indicates that perhaps the ergodic hypothesis is a too strong requirement.

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Yildirim, O. Ozgur, et Donhee Ham. « High-dimensional chaos from self-sustained collisions of solitons ». Applied Physics Letters 104, n^o 24 (16 juin 2014) : 244109. http://dx.doi.org/10.1063/1.4884943.

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Wang, Cong, Hongli Zhang, Wenhui Fan et Ping Ma. « Analysis of chaos in high-dimensional wind power system ». Chaos : An Interdisciplinary Journal of Nonlinear Science 28, n^o 1 (janvier 2018) : 013102. http://dx.doi.org/10.1063/1.5003464.

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GRASSI, GIUSEPPE, et SAVERIO MASCOLO. « SYNCHRONIZATION OF HIGH-DIMENSIONAL CHAOS GENERATORS BY OBSERVER DESIGN ». International Journal of Bifurcation and Chaos 09, n^o 06 (juin 1999) : 1175–80. http://dx.doi.org/10.1142/s0218127499000821.

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In this Letter a method for synchronizing hyperchaotic systems described by ordinary differential equations (ODEs) as well as functional differential equations (FDEs) is illustrated. The technique, which exploits the concept of observer from system theory, is at first applied for synchronizing an example of high-order circuit. A remarkable feature is that hyperchaos synchronization is achieved via a scalar signal. Successively, the tool is applied for synchronizing an example of high-dimensional chaos generator, represented by a cell equation in Cellular Neural Networks with delay. Finally, the advantages of the proposed approach are discussed in detail.

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Löcher, M., et E. R. Hunt. « Control of High-Dimensional Chaos in Systems with Symmetry ». Physical Review Letters 79, n^o 1 (7 juillet 1997) : 63–66. http://dx.doi.org/10.1103/physrevlett.79.63.

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HU, BAMBI, et ZHIGANG ZHENG. « PHASE SYNCHRONIZATIONS : TRANSITIONS FROM HIGH- TO LOW-DIMENSIONAL TORI THROUGH CHAOS ». International Journal of Bifurcation and Chaos 10, n^o 10 (octobre 2000) : 2399–414. http://dx.doi.org/10.1142/s0218127400001535.

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Phase synchronized entrainment of coupled nonidentical limit cycles and chaotic oscillators is a generic phenomenon in complicated and chaotic dynamics. Recent developments in phase synchronization are reviewed. Two approaches: The statistical approach and the dynamical approach are proposed. From a statistical viewpoint, phase entrainment exhibits a nonequilibrium phase transition from the disordered state to the ordered state. Dynamically, phase synchronization among oscillators shows a tree-like bifurcation and a number of clustered states are experienced. The route from partial to complete phase synchronization for coupled limit cycles is identified as a cascade of transitions from high- to low-dimensional tori (quasiperiodicity) interrupted by intermittent chaos. For coupled periodic oscillators, desynchronization-induced chaos originates from the mixing of intermittent ON–OFF duration time scales. For coupled chaotic cases, the route to phase entrainment is identified as transitions from high- to low-dimensional chaos.

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Ryabov, Vladimir, et Dmitry Nerukh. « Statistical Complexity of Low- and High-Dimensional Systems ». Journal of Atomic, Molecular, and Optical Physics 2012 (20 juin 2012) : 1–6. http://dx.doi.org/10.1155/2012/589651.

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We suggest a new method for the analysis of experimental time series that can distinguish high-dimensional dynamics from stochastic motion. It is based on the idea of statistical complexity, that is, the Shannon entropy of the so-called ϵ-machine (a Markov-type model of the observed time series). This approach has been recently demonstrated to be efficient for making a distinction between a molecular trajectory in water and noise. In this paper, we analyse the difference between chaos and noise using the Chirikov-Taylor standard map as an example in order to elucidate the basic mechanism that makes the value of complexity in deterministic systems high. In particular, we show that the value of statistical complexity is high for the case of chaos and attains zero value for the case of stochastic noise. We further study the Markov property of the data generated by the standard map to clarify the role of long-time memory in differentiating the cases of deterministic systems and stochastic motion.

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Molnár, Márk. « Low-dimensional versus high-dimensional chaos in brain function – is it an and/or issue ? » Behavioral and Brain Sciences 24, n^o 5 (octobre 2001) : 823–24. http://dx.doi.org/10.1017/s0140525x01370097.

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We discuss whether low-dimensional chaos and even nonlinear processes can be traced in the electrical activity of the brain. Experimental data show that the dimensional complexity of the EEG decreases during event-related potentials associated with cognitive effort. This probably represents increased nonlinear cooperation between different neural systems during sensory information processing.

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Zhang, Xing. « Multimedia Image Encryption Analysis Based on High-Dimensional Chaos Algorithm ». Advances in Multimedia 2021 (20 décembre 2021) : 1–8. http://dx.doi.org/10.1155/2021/7384170.

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With the development of network and multimedia technology, multimedia communication has attracted the attention of researchers. Image encryption has become an urgent need for secure multimedia communication. Compared with the traditional encryption system, encryption algorithms based on chaos are easier to implement, which makes them more suitable for large-scale data encryption. The calculation method of image encryption proposed in this paper is a combination of high-dimensional chaotic systems. This algorithm is mainly used for graph mapping and used the Lorenz system to expand and replace them one by one. Studies have shown that this calculation method causes mixed pixel values, good diffusion performance, and strong key performance with strong resistance. The pixel of the encrypted picture is distributed relatively random, and the characteristics of similar loudness are not relevant. It is proved through experiments that the above calculation methods have strong safety performance.

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Al-Obeidi, Ahmed S., et Saad Fawzi Al-Azzawi. « Hybrid synchronization of high-dimensional chaos with self-excited attractors ». Journal of Interdisciplinary Mathematics 23, n^o 8 (30 août 2020) : 1569–84. http://dx.doi.org/10.1080/09720502.2020.1776941.

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Reyl, C., L. Flepp, R. Badii et E. Brun. « Control of NMR-laser chaos in high-dimensional embedding space ». Physical Review E 47, n^o 1 (1 janvier 1993) : 267–72. http://dx.doi.org/10.1103/physreve.47.267.

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Christini, David J., James J. Collins et Paul S. Linsay. « Experimental control of high-dimensional chaos : The driven double pendulum ». Physical Review E 54, n^o 5 (1 novembre 1996) : 4824–27. http://dx.doi.org/10.1103/physreve.54.4824.

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Eckhardt, Bruno. « Turbulence Transition in Shear Flows : Chaos in High-Dimensional Spaces ». Procedia IUTAM 5 (2012) : 165–68. http://dx.doi.org/10.1016/j.piutam.2012.06.021.

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Anbang Wang, Bingjie Wang, Lei Li, Yuncai Wang et K. Alan Shore. « Optical Heterodyne Generation of High-Dimensional and Broadband White Chaos ». IEEE Journal of Selected Topics in Quantum Electronics 21, n^o 6 (novembre 2015) : 531–40. http://dx.doi.org/10.1109/jstqe.2015.2427253.

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Ciofini, M., A. Labate, R. Meucci et F. T. Arecchi. « Experimental control of chaos in a delayed high-dimensional system ». European Physical Journal D - Atomic, Molecular and Optical Physics 7, n^o 1 (1 août 1999) : 5–9. http://dx.doi.org/10.1007/s100530050340.

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Pazó, D., et M. A. Matías. « Direct transition to high-dimensional chaos through a global bifurcation ». Europhysics Letters (EPL) 72, n^o 2 (octobre 2005) : 176–82. http://dx.doi.org/10.1209/epl/i2005-10239-3.

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He, Wanxin, Yan Zeng et Gang Li. « An adaptive polynomial chaos expansion for high-dimensional reliability analysis ». Structural and Multidisciplinary Optimization 62, n^o 4 (1 juillet 2020) : 2051–67. http://dx.doi.org/10.1007/s00158-020-02594-4.

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Kassner, Klaus, Chaouqi Misbah, Heiner Müller-Krumbhaar et Alexandre Valance. « Directional solidification at high speed. II. Transition to chaos ». Physical Review E 49, n^o 6 (1 juin 1994) : 5495–516. http://dx.doi.org/10.1103/physreve.49.5495.

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Heiss, W. D., et A. A. Kotz�. « A one dimensional model f�r quantum Chaos ». Zeitschrift f�r Physik A Atomic Nuclei 335, n^o 2 (juin 1990) : 131–37. http://dx.doi.org/10.1007/bf01294467.

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Gundlach, V. M., et D. A. Rand. « Spatio-temporal chaos. II. Unique Gibbs states for higher-dimensional symbolic systems ». Nonlinearity 6, n^o 2 (1 mars 1993) : 201–13. http://dx.doi.org/10.1088/0951-7715/6/2/003.

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PROTOPOPESCU, V., et Y. Y. AZMY. « TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS ». Mathematical Models and Methods in Applied Sciences 02, n^o 01 (mars 1992) : 79–90. http://dx.doi.org/10.1142/s0218202592000065.

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We construct an example of linear rate equation in the Banach space of summable sequences, l1, that exhibits the three properties required as signature of topological chaos, namely: (i) topological transitivity, (ii) dense periodic orbits, and (iii) positive Lyapunov exponents. The example is based on the properties of the backward shift operator on the Banach space l1. Since linear chaos in the sense described above can occur only in an infinite-dimensional setting, possible finite-dimensional approximate manifestations are investigated. The relationship between the linear backward shift and the nonlinear Bernoulli shift is also discussed.

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Levy, Jeremy, Mark S. Sherwin et James Theiler. « Low-dimensional chaos and high-dimensional behavior in the switching charge-density-wave conductorNbSe3 ». Physical Review B 48, n^o 11 (15 septembre 1993) : 7857–65. http://dx.doi.org/10.1103/physrevb.48.7857.

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MAISTRENKO, VOLODYMYR, ANNA VASYLENKO, YURI MAISTRENKO et ERIK MOSEKILDE. « PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL ». International Journal of Bifurcation and Chaos 20, n^o 06 (juin 2010) : 1811–23. http://dx.doi.org/10.1142/s0218127410026861.

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The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic attractors. We also study the subcritical frequency-splitting bifurcation at the onset of desynchronization and demonstrate that the transition to phase chaos takes place via a torus destruction process.

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JING, ZHUJUN, et JIANPING YANG. « COMPLEX DYNAMICS IN PENDULUM EQUATION WITH PARAMETRIC AND EXTERNAL EXCITATIONS II ». International Journal of Bifurcation and Chaos 16, n^o 10 (octobre 2006) : 3053–78. http://dx.doi.org/10.1142/s0218127406016653.

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This paper (II) is a continuation of "Complex dynamics in pendulum equation with parametric and external excitations (I)." By applying second-order averaging method and Melnikov's method, we obtain the criterion of existence of chaos in an averaged system under quasi-periodic perturbation for Ω = nω + ∊ν, n = 1, 2, 4 and cannot prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for Ω = nω + ∊ν, n = 3, 5–15 by Melnikov's method, where ν is not rational to ω. However, we show the occurrence of chaos in the averaged and original systems under quasi-periodic perturbation for Ω = nω + ∊ν, n = 3, 5 by numerical simulation. The numerical simulations, include the bifurcation diagram of fixed points, bifurcation diagrams in three- and two-dimensional spaces, homoclinic bifurcation surface, maximum Lyapunov exponent, phase portraits, Poincaré map, are plotted to illustrate theoretical analysis, and to expose the complex dynamical behaviors, including period-3 orbits in different chaotic regions, interleaving occurrence of chaotic behaviors and quasi-periodic behaviors, a different kind of interior crisis, jumping behavior of quasi-periodic sets, different nice quasi-periodic attractors, nonchaotic attractors and chaotic attractors, coexistence of three quasi-periodic sets, onset of chaos which occurs more than once for a given external frequency or amplitudes, and quasi-periodic route to chaos. We do not find the period-doubling cascade. The dynamical behaviors under quasi-periodic perturbation are different from that of periodic perturbation.

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Fang, Pan, Liming Dai, Yongjun Hou, Mingjun Du et Wang Luyou. « The Study of Identification Method for Dynamic Behavior of High-Dimensional Nonlinear System ». Shock and Vibration 2019 (7 mars 2019) : 1–9. http://dx.doi.org/10.1155/2019/3497410.

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The dynamic behavior of nonlinear systems can be concluded as chaos, periodicity, and the motion between chaos and periodicity; therefore, the key to study the nonlinear system is identifying dynamic behavior considering the different values of the system parameters. For the uncertainty of high-dimensional nonlinear dynamical systems, the methods for identifying the dynamics of nonlinear nonautonomous and autonomous systems are treated. In addition, the numerical methods are employed to determine the dynamic behavior and periodicity ratio of a typical hull system and Rössler dynamic system, respectively. The research findings will develop the evaluation method of dynamic characteristics for the high-dimensional nonlinear system.

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Mirus, K. A., et J. C. Sprott. « Controlling chaos in a high dimensional system with periodic parametric perturbations ». Physics Letters A 254, n^o 5 (avril 1999) : 275–78. http://dx.doi.org/10.1016/s0375-9601(99)00068-7.

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