It is very important to generate hyperchaos with more complicated dynamics as a model for theoretical research and practical application. A new hyperchaotic system with double piecewise-linear functions in state equations is presented and physically implemented by circuit design. Based on the theoretical analyses and simulations, the hyperchaotic dynamical properties of this nonlinear system are revealed by equilibria, Lyapunov exponents, and bifurcations, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.
Issue Section:
Research Papers
Keywords:
Stability
References
1.
Matsumoto
, T.
, Chua
, L. O.
, and Kobayashi
, K.
, 1986
, “Hyperchaos: Laboratory Experiment and Numerical Confirmation
,” IEEE Trans. Circuits Syst.
, 33
(11
), pp. 1143
–1147
.10.1109/TCS.1986.10858622.
Mahmoud
, G. M.
, Mahmoud
, E. E.
, and Arafa
, A. A.
, 2013
, “Controlling Hyperchaotic Complex Systems With Unknown Parameters Based on Adaptive Passive Method
,” Chin. Phys. B.
, 22
(6
), p. 060508
.10.1088/1674-1056/22/6/0605083.
Wang
, Z. S.
, and Zhang
, H. G.
, 2013
, “Synchronization Stability in Complex Interconnected Neural Networks With Nonsymmetric Coupling
,” Neurocomputing
, 108
(5), pp. 84
–92
.10.1016/j.neucom.2012.11.0144.
Wang
, H.
, Han
, Z. Z.
, Xie
, Q. Y.
, and Zhang
, W.
, 2009
, “Finite-Time Chaos Synchronization of Unified Chaotic System With Uncertain Parameters
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
(5
), pp. 2239
–2247
.10.1016/j.cnsns.2008.04.0155.
Zhang
, Y. Q.
, and Wang
, X. Y.
, 2014
, “A Symmetric Image Encryption Algorithm Based on Mixed Linear–Nonlinear Coupled Map Lattice
,” Inf. Sci.
, 273
(7), pp. 329
–351
.10.1016/j.ins.2014.02.1566.
Liu
, H. J.
, Wang
, X. Y.
, and Zhu
, Q. L.
, 2011
, “Asynchronous Anti-Noise Hyper Chaotic Secure Communication System Based on Dynamic Delay and State Variables Switching
,” Phys. Lett. A
, 375
(30–31
), pp. 2828
–2835
.10.1016/j.physleta.2011.06.0297.
Wang
, X.
, and Chen
, G. R.
, 2013
, “Constructing a Chaotic System With Any Number of Equilibria
,” Nonlinear Dyn.
, 71
(3
), pp. 429
–436
.10.1007/s11071-012-0669-78.
Zheng
, S.
, Dong
, G. G.
, and Bi
, Q. S.
, 2010
, “A New Hyperchaotic System and Its Synchronization
,” Appl. Math. Comput.
, 215
(9
), pp. 3192
–3200
.10.1016/j.amc.2009.09.0609.
Liu
, W. B.
, Tang
, W. K. S.
, and Chen
, G. R.
, 2011
, “Forming and Implementing a Hyperchaotic System With Rich Dynamics
,” Chin. Phys. B.
, 20
(9
), p. 090510
.10.1088/1674-1056/20/9/09051010.
Han
, Q.
, Liu
, C. X.
, Sun
, L.
, and Zhu
, D. R.
, 2013
, “A Fractional Order Hyperchaotic System Derived From a Liu System and Its Circuit Realization
,” Chin. Phys. B.
, 22
(2
), p. 020502
.10.1088/1674-1056/22/2/02050211.
Rössler
, O. E.
, 1979
, “An Equation for Hyperchaos
,” Phys. Lett. A.
, 71
(2,3
), pp. 155
–157
.10.1016/0375-9601(79)90150-612.
Wang
, X. Y.
, and Wang
, M. J.
, 2007
, “Hyperchaotic Lorenz System
,” Acta Phys. Sin.
, 56
(9
), pp. 5136
–5141
. Available at: http://wulixb.iphy.ac.cn/CN/volumn/home.shtml13.
Qi
, G. Y.
, Du
, S. Z.
, Chen
, G. R.
, Chen
, Z. Q.
, and Yuan
, Z. Z.
, 2005
, “On a Four-Dimensional Chaotic System
,” Chaos, Solitons Fractals
, 23
(5
), pp. 1671
–1682
.10.1016/j.chaos.2004.06.05414.
Saito
, T.
, 1990
, “An Approach Toward Higher Dimensional Hysteresis Chaos Generator
,” IEEE Trans. Circuits Syst.
, 37
(3
), pp. 399
–409
.10.1109/31.5273315.
Yu
, S. M.
, Lü
, J. H.
, and Chen
, G. R.
, 2007
, “A Family of n-Scroll Hyperchaotic Attractors and Their Realization
,” Phys. Lett. A
, 364
(3–4
), pp. 244
–251
.10.1016/j.physleta.2006.12.02916.
Yalcin
, M. E.
, Suykens
, J. A. K.
, and Vandewalle
, J. P. L.
, 2005
, Cellular Neural Networks, Multi-Scroll Chaos and Synchronization
, World Scientific
, Singapore
, Chap. 4.17.
Lü
, J. H.
, and Chen
, G. R.
, 2006
, “Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications
,” Int. J. Bifurc. Chaos.
, 16
(4
), pp. 775
–858
.10.1142/S021812740601517918.
Zhang
, Y. Q.
, and Wang
, X. Y.
, 2014
, “Spatiotemporal Chaos in Mixed Linear–Nonlinear Coupled Logistic Map Lattice
,” Physica A
, 402
(5), pp. 104
–118
.10.1016/j.physa.2014.01.05119.
Zhang
, Y. Q.
, and Wang
, X. Y.
, 2013
, “Spatiotemporal Chaos in Arnold Coupled Logistic Map Lattice
,” Nonlinear Anal. Model. Control
, 18
(4
), pp. 526
–541
. Available at: http://www.mii.lt/NA/20.
Teng
, L.
, Iu
, H. H. C.
, Wang
, X. Y.
, and Wang
, X. K.
, 2014
, “Chaotic Behavior in Fractional-Order Memristor-Based Simplest Chaotic Circuit Using Fourth Degree Polynomial
,” Nonlinear Dyn.
, 77
(1–2
), pp. 231
–241
.10.1007/s11071-014-1286-421.
Fitch
, A. L.
, Yu
, D.
, Iu
, H. H. C.
, and Sreeram
, V.
, 2012
, “Hyperchaos in a Memristor-Based Modified Canonical Chua's Circuit
,” Int. J. Bifurc. Chaos
, 22
(6
), p. 1250133
.10.1142/S021812741250133722.
Niu
, Y. J.
, Wang
, X. Y.
, Wang
, M. J.
, and Zhang
, H. G.
, 2010
, “A New Hyperchaotic System and Its Circuit Implementation
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(11
), pp. 3518
–3524
.10.1016/j.cnsns.2009.08.01423.
Wang
, X. Y.
, and Wang
, M. J.
, 2008
, “A Hyperchaos Generated From Lorenz System
,” Physica A
, 387
(14
), pp. 3751
–3758
.10.1016/j.physa.2008.02.02024.
Barboza
, R.
, 2008
, “Hyperchaos in a Chua's Circuit With Two New Added Branches
,” Int. J. Bifurc. Chaos.
, 18
(4
), pp. 1151
–1159
.10.1142/S021812740802088425.
Matsumoto
, T.
, Chua
, L. O.
, and Komuro
, M.
, 1985
, “The Double Scroll
,” IEEE Trans. Circuits Syst.
, 32
(8
), pp. 798
–818
.10.1109/TCS.1985.108579126.
Wolf
, A.
, Swift
, J. B.
, Swinney
, H. L.
, and Vastano
, J. A.
, 1985
, “Determining Lyapunov Exponents From a Time Series
,” Physica D
, 16
(3
), pp. 285
–317
.10.1016/0167-2789(85)90011-9Copyright © 2015 by ASME
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