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Journal articles on the topic 'Chaotic behvaior in systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

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1

Ping, Zhou, Cheng Yuan-Ming, and Kuang Fei. "Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)." Chinese Physics B 19, no. 9 (2010): 090503. http://dx.doi.org/10.1088/1674-1056/19/9/090503.

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2

Altmann, Eduardo G., Jefferson S. E. Portela, and Tamás Tél. "Leaking chaotic systems." Reviews of Modern Physics 85, no. 2 (2013): 869–918. http://dx.doi.org/10.1103/revmodphys.85.869.

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3

Chlouverakis, Konstantinos E., and J. C. Sprott. "Chaotic hyperjerk systems." Chaos, Solitons & Fractals 28, no. 3 (2006): 739–46. http://dx.doi.org/10.1016/j.chaos.2005.08.019.

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4

Freckleton, Rob P. "Chaotic mating systems." Trends in Ecology & Evolution 17, no. 11 (2002): 493–95. http://dx.doi.org/10.1016/s0169-5347(02)02626-5.

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5

Jafari, Sajad, and Tomasz Kapitaniak. "Special chaotic systems." European Physical Journal Special Topics 229, no. 6-7 (2020): 877–86. http://dx.doi.org/10.1140/epjst/e2020-000017-y.

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6

Zhou, Ping, and Rui Ding. "Chaotic synchronization between different fractional-order chaotic systems." Journal of the Franklin Institute 348, no. 10 (2011): 2839–48. http://dx.doi.org/10.1016/j.jfranklin.2011.09.004.

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7

USHIO, Toshimitsu. "Control of Chaotic Systems." Journal of Japan Society for Fuzzy Theory and Systems 7, no. 3 (1995): 475–85. http://dx.doi.org/10.3156/jfuzzy.7.3_475.

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8

Zakharov, Ivan S., S. I. Ilyin, V. M. Dovgal, and I. A. Saraev. "Chaotic Systems: Automaton Model." Telecommunications and Radio Engineering 69, no. 3 (2010): 207–12. http://dx.doi.org/10.1615/telecomradeng.v69.i3.20.

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9

Pecora, Louis M., and Thomas L. Carroll. "Synchronization in chaotic systems." Physical Review Letters 64, no. 8 (1990): 821–24. http://dx.doi.org/10.1103/physrevlett.64.821.

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10

Tanner, Gregor, and Dieter Wintgen. "Quantization of chaotic systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 2, no. 1 (1992): 53–59. http://dx.doi.org/10.1063/1.165897.

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11

Vaidya, P. G., and Rong He. "Designing synchronous chaotic systems." Journal of the Acoustical Society of America 92, no. 4 (1992): 2475. http://dx.doi.org/10.1121/1.404439.

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12

Chen, Y. Y. "Randomly Synchronizing Chaotic Systems." Progress of Theoretical Physics 96, no. 4 (1996): 683–92. http://dx.doi.org/10.1143/ptp.96.683.

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13

Miranda, Annamaria. "Lightly chaotic dynamical systems." Applied General Topology 25, no. 2 (2024): 277–89. http://dx.doi.org/10.4995/agt.2024.15293.

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In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of light chaos is the most significant. Several examples, which clarify the relationships between this kind of chaos and some classical notions, are given. Particular attention is also devoted to the connections between the dynamical properties of a system and the dynamical properties of the associated functional envelope. We show, among other things, that a continuous map f : X → X , where X is a metric space, is chaotic (in the sense of Devaney) if and only if the associate

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14

VIANA, R. L., S. E. DE S. PINTO, J. R. R. BARBOSA, and C. GREBOGI. "PSEUDO-DETERMINISTIC CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 13, no. 11 (2003): 3235–53. http://dx.doi.org/10.1142/s0218127403008636.

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We call a chaotic dynamical system pseudo-deterministic when it does not produce numerical, or pseudo-trajectories that stay close, or shadow chaotic true trajectories, even though the model equations are strictly deterministic. In this case, single chaotic trajectories may not be meaningful, and only statistical predictions, at best, could be drawn on the model, like in a stochastic system. The dynamical reason for this behavior is nonhyperbolicity characterized either by tangencies of stable and unstable manifolds or by the presence of periodic orbits embedded in a chaotic invariant set with

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15

Pecora, Louis M., and Thomas L. Carroll. "Synchronization of chaotic systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 25, no. 9 (2015): 097611. http://dx.doi.org/10.1063/1.4917383.

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16

Grebogi, Celso, and Ying-Cheng Lai. "Controlling chaotic dynamical systems." Systems & Control Letters 31, no. 5 (1997): 307–12. http://dx.doi.org/10.1016/s0167-6911(97)00046-7.

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17

Romeiras, Filipe J., Celso Grebogi, Edward Ott, and W. P. Dayawansa. "Controlling chaotic dynamical systems." Physica D: Nonlinear Phenomena 58, no. 1-4 (1992): 165–92. http://dx.doi.org/10.1016/0167-2789(92)90107-x.

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18

Carroll, T. L., and L. M. Pecora. "Cascading synchronized chaotic systems." Physica D: Nonlinear Phenomena 67, no. 1-3 (1993): 126–40. http://dx.doi.org/10.1016/0167-2789(93)90201-b.

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19

Pompe, B., and R. W. Leven. "Transinformation of Chaotic Systems." Physica Scripta 34, no. 1 (1986): 8–13. http://dx.doi.org/10.1088/0031-8949/34/1/002.

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20

Vaidya, P. G., Rong He, and M. J. Anderson. "Synchronization of chaotic systems." Journal of the Acoustical Society of America 88, S1 (1990): S195. http://dx.doi.org/10.1121/1.2028875.

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21

Savvidy, George. "Maximally chaotic dynamical systems." Annals of Physics 421 (October 2020): 168274. http://dx.doi.org/10.1016/j.aop.2020.168274.

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22

Young, Lai-Sang. "Understanding Chaotic Dynamical Systems." Communications on Pure and Applied Mathematics 66, no. 9 (2013): 1439–63. http://dx.doi.org/10.1002/cpa.21468.

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23

Yoshida, Katsutoshi, Keijin Sato, Sumio Yamamoto, and Kazutaka Yokota. "Identification of Nonlinear Systems by Synchronization in Chaotic Systems. Index of Synchronization in Chaotic Systems." Transactions of the Japan Society of Mechanical Engineers Series C 60, no. 578 (1994): 3268–73. http://dx.doi.org/10.1299/kikaic.60.3268.

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24

MACAU, E. E. N., and C. GREBOGI. "DRIVING TRAJECTORIES IN CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 11, no. 05 (2001): 1423–42. http://dx.doi.org/10.1142/s0218127401002808.

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This work presents the main ideas and the fundamental procedures for guiding trajectories on chaotic systems and for stabilizing chaotic orbits, all with the use of small perturbations. We consider an extension of the Ott–Grebogi–Yorke method of controlling chaos and an associated procedure for guiding trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattractive. As nonattractive chaotic invariant sets commonly exist embedded in high dimensional systems, we also argue that we can combine chaotic control

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25

CUOMO, KEVIN M. "SYNTHESIZING SELF-SYNCHRONIZING CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 03, no. 05 (1993): 1327–37. http://dx.doi.org/10.1142/s0218127493001082.

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A systematic approach is developed for synthesizing N-dimensional dissipative chaotic systems which possess the self-synchronization property. The ability to synthesize new chaotic systems further enhances the usefulness of synchronized chaotic systems for communications.

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26

Shu-Bo, Liu, Sun Jing, Xu Zheng-Quan, and Liu Jin-Shuo. "Digital chaotic sequence generator based on coupled chaotic systems." Chinese Physics B 18, no. 12 (2009): 5219–27. http://dx.doi.org/10.1088/1674-1056/18/12/019.

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27

LU, HONGTAO, and WALLACE K. S. TANG. "CHAOTIC PHASE SHIFT KEYING IN DELAYED CHAOTIC ANTICONTROL SYSTEMS." International Journal of Bifurcation and Chaos 12, no. 05 (2002): 1017–28. http://dx.doi.org/10.1142/s0218127402004887.

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Based on the delayed feedback chaotic anticontrol systems, a new chaotic phase shift keying (CPSK) scheme is proposed for secure communications in this paper. The chaotic transmitter is a linear system with nonlinear delayed feedback in which a trigonometric function cos(·) is used. Such system can exhibit rich chaotic behavior with the choice of appropriate parameters. For an M-ary communication system where M=2n, each of these M possible symbols (n-bits) is firstly mapped to 2(m-1)π/M (with m=1, 2, …, M) which is used as the phase argument for the cos(·) function in the nonlinear feedback. T

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28

Morgül, Ömer, and Moez Feki. "A chaotic masking scheme by using synchronized chaotic systems." Physics Letters A 251, no. 3 (1999): 169–76. http://dx.doi.org/10.1016/s0375-9601(98)00868-8.

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29

Li, Lixiang, Yixian Yang, Haipeng Peng, and Xiangdong Wang. "Parameters identification of chaotic systems via chaotic ant swarm." Chaos, Solitons & Fractals 28, no. 5 (2006): 1204–11. http://dx.doi.org/10.1016/j.chaos.2005.04.110.

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30

Custódio, M. S., C. Manchein, and M. W. Beims. "Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 22, no. 2 (2012): 026112. http://dx.doi.org/10.1063/1.3697985.

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31

Jiu-Chao, Feng, and Qiu Yu-Hui. "Identification of Chaotic Systems with Application to Chaotic Communication." Chinese Physics Letters 21, no. 2 (2004): 250–53. http://dx.doi.org/10.1088/0256-307x/21/2/010.

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32

Jun-hai, Ma, Ren Biao, and Chen Yu-shu. "Impulsive control of chaotic attractors in nonlinear chaotic systems." Applied Mathematics and Mechanics 25, no. 9 (2004): 971–76. http://dx.doi.org/10.1007/bf02438345.

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33

Ping, Zhou, and Cao Yu-Xia. "Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems." Chinese Physics B 19, no. 10 (2010): 100507. http://dx.doi.org/10.1088/1674-1056/19/10/100507.

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34

Zhang, Xiao-Qing, Jian Xiao, and Qing Zhang. "Dislocated projective synchronization between fractional-order chaotic systems and integer-order chaotic systems." Optik 130 (February 2017): 1139–50. http://dx.doi.org/10.1016/j.ijleo.2016.11.118.

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35

Sun, Junwei, Yi Shen, and Guangzhao Cui. "Compound Synchronization of Four Chaotic Complex Systems." Advances in Mathematical Physics 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/921515.

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The chaotic complex system is designed from the start of the chaotic real system. Dynamical properties of a chaotic complex system in complex space are investigated. In this paper, a compound synchronization scheme is achieved for four chaotic complex systems. According to Lyapunov stability theory and the adaptive control method, four chaotic complex systems are considered and the corresponding controllers are designed to realize the compound synchronization scheme. Four novel design chaotic complex systems are given as an example to verify the validity and feasibility of the proposed control

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36

SIRA-RAMÍREZ, HEBERTT, and CÉSAR CRUZ-HERNÁNDEZ. "SYNCHRONIZATION OF CHAOTIC SYSTEMS: A GENERALIZED HAMILTONIAN SYSTEMS APPROACH." International Journal of Bifurcation and Chaos 11, no. 05 (2001): 1381–95. http://dx.doi.org/10.1142/s0218127401002778.

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A reapproach to chaotic systems synchronization is presented from the perspective of passivity-based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector fields. The synchronization and lack of synchronization of several well-studied chaotic systems is reexplained in these terms.

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37

Landa, P. S., and M. G. Rosenblum. "Synchronization and Chaotization of Oscillations in Coupled Self-Oscillating Systems." Applied Mechanics Reviews 46, no. 7 (1993): 414–26. http://dx.doi.org/10.1115/1.3120370.

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The effects of synchronization of chaotic and periodic self-oscillation systems are discussed. Two mechanisms of synchronization of periodic systems which manifest themselves at synchronization of chaotic systems are determinated. Examples of synchronization of chaotic systems by harmonic external force, mutual synchronization of periodic and chaotic systems, as well as of mutual synchronization of two and more chaotic systems are discussed.

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38

Wu, Tiantian, Qingdu Li, and Xiao-Song Yang. "Designing Chaotic Systems by Piecewise Affine Systems." International Journal of Bifurcation and Chaos 26, no. 09 (2016): 1650154. http://dx.doi.org/10.1142/s0218127416501546.

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Based on mathematical analysis, this paper provides a methodology to ensure the existence of homoclinic orbits in a class of three-dimensional piecewise affine systems. In addition, two chaotic generators are provided to illustrate the effectiveness of the method.

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39

Khaleel, Amal Hameed, and Iman Q. Abduljaleel. "Chaotic Image Cryptography Systems: A Review." Samarra Journal of Pure and Applied Science 3, no. 2 (2021): 129–43. http://dx.doi.org/10.54153/sjpas.2021.v3i2.244.

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In recent decades, image encryption has been a popular and important field of research. The image encryption techniques have been studied thoroughly to ensure the safety of digital images on transmission through the networks. A large range of algorithms for chaotic-based cryptographic systems has been suggested and submitted to enhance the efficiency of the encryption methods. The chaotic map is one technique to guarantee security. The benefits of chaotic image encryption include the fact that it is simple to implement; it has a faster encryption speed, and it is powerful against attacks. Due

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40

Wang, Chuanfu, Chunlei Fan, and Qun Ding. "Constructing Discrete Chaotic Systems with Positive Lyapunov Exponents." International Journal of Bifurcation and Chaos 28, no. 07 (2018): 1850084. http://dx.doi.org/10.1142/s0218127418500840.

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The chaotic system is widely used in chaotic cryptosystem and chaotic secure communication. In this paper, a universal method for designing the discrete chaotic system with any desired number of positive Lyapunov exponents is proposed to meet the needs of hyperchaotic systems in chaotic cryptosystem and chaotic secure communication, and three examples of eight-dimensional discrete system with chaotic attractors, eight-dimensional discrete system with fixed point attractors and eight-dimensional discrete system with periodic attractors are given to illustrate how the proposed methods control th

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41

Wang, Chuanfu, and Qun Ding. "A Class of Quadratic Polynomial Chaotic Maps and Their Fixed Points Analysis." Entropy 21, no. 7 (2019): 658. http://dx.doi.org/10.3390/e21070658.

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When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic construction theory, the construction of chaotic systems mainly depends on the exhaustive search of systematic parameters or initial values, especially for a class of dynamical systems with hidden chaotic attractors. In this paper, a class of quadratic polynomial chaotic maps is studied, and a general method for constructing quadratic polynomial chaotic m

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42

Wang, Xiaoyuan, Xue Zhang, and Meng Gao. "A Novel Voltage-Controlled Tri-Valued Memristor and Its Application in Chaotic System." Complexity 2020 (July 25, 2020): 1–8. http://dx.doi.org/10.1155/2020/6949703.

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Memristor is a kind of passive nonlinear element, which is widely used in nonlinear systems, especially chaotic systems, because of its nanometer size, nonvolatile property, and good nonlinear characteristics. Compared with general chaotic systems, chaotic systems based on memristors have richer dynamic characteristics. However, the current research mainly focuses on the binary and continuous chaotic systems based on memristors, and studies on the tri-valued and multi-valued memristor chaotic systems are relative scarce. For this reason, a mathematical model of tri-valued memristor is proposed

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43

Li, Bo, Xiaobing Zhou, and Yun Wang. "Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems." Complexity 2019 (November 7, 2019): 1–9. http://dx.doi.org/10.1155/2019/5184032.

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Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic syste

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44

Aurich, R., A. Bäcker, and F. Steiner. "Mode Fluctuations as Fingerprints of Chaotic and Non-Chaotic Systems." International Journal of Modern Physics B 11, no. 07 (1997): 805–49. http://dx.doi.org/10.1142/s0217979297000459.

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The mode-fluctuation distribution P(W) is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the E(k,L) functions being the probability of finding k energy levels in a randomly chosen interval of length L, and the distribution of n(L), where n(L) is the number of levels in such an interval, and their cumulants ck(L). It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants Ck, k ≥ 3, implies a Gaussian behaviour of

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45

Murugesan, Regan, Suresh Rasappan, Pugalarasu Rajan, and Sathish Kumar Kumaravel. "Synchronization of Liu-Su-Liu and Liu-Chen-Liu Chaotic Systems by Nonlinear Feedback Control." Journal of Computational and Theoretical Nanoscience 16, no. 12 (2019): 4903–7. http://dx.doi.org/10.1166/jctn.2019.8540.

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This paper investigates the global chaos synchronization of identical Liu-Su-Liu chaotic systems (2006) and non-identical Liu-Su-Liu chaotic system (2006) and Liu-Chen-Liu chaotic system (2007). In this paper, active nonlinear control method has been successfully applied to synchronize two identical Liu-Su-Liu chaotic systems and then to synchronize two different chaotic systems, viz. Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to synchronize Liu-Su-Liu and Liu

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46

Short, Kevin M., and Matthew A. Morena. "Signatures of Quantum Mechanics in Chaotic Systems." Entropy 21, no. 6 (2019): 618. http://dx.doi.org/10.3390/e21060618.

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We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external contro

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47

Guo, Yali, Han Zhang, Liang Wang, Huawei Fan, Jinghua Xiao, and Xingang Wang. "Transfer learning of chaotic systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 1 (2021): 011104. http://dx.doi.org/10.1063/5.0033870.

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48

Kamil, I. A. "Self-Synchronization in Chaotic Systems." Journal of Engineering and Applied Sciences 7, no. 6 (2012): 411–17. http://dx.doi.org/10.3923/jeasci.2012.411.417.

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49

Rocha, J. L., S. Aleixo, and A. Caneco. "Synchronization in Richards’ Chaotic Systems." Journal of Applied Nonlinear Dynamics 3, no. 2 (2014): 115–30. http://dx.doi.org/10.5890/jand.2014.06.002.

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50

Genger, T. K., T. J. Anande, and S. Al-Shehri. "Computer Simulation of Chaotic Systems." International Journal of Applied Information Systems 12, no. 1 (2017): 1–8. http://dx.doi.org/10.5120/ijais2017451605.

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