A new three-dimensional chaotic system: Dynamical properties and simulation

Abstract This paper recomends a new three-dimensional autonomous chaotic system with six terms including three multipliers, which is different from the Lorenz system and other existing systems. Basic dynamical characteristics of this new system are analyzed via equilibria, Lyapunov exponent spectrum, a dissipative system, phase portraits, the Poincare map, bifurcation diagrams and Hopf bifurcation. The compound structures of this new system are also investigated. Analysis of the results show that this chaotic attractor has complex dynamics with some interesting characteristics.

[1]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[2]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[3]  Recai Kiliç,et al.  A new nonautonomous version of Chua's circuit: Experimental observations , 2006, J. Frankl. Inst..

[4]  P. Cai,et al.  Hopf bifurcation and chaos control in a new chaotic system via hybrid control strategy , 2017 .

[5]  Vijay K. Yadav,et al.  Stability analysis, chaos control of a fractional order chaotic chemical reactor system and its function projective synchronization with parametric uncertainties , 2017 .

[6]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[7]  Zhi-Hong Guan,et al.  Chaotification for a class of cellular neural networks with distributed delays , 2011 .

[8]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[9]  Guanrong Chen,et al.  The compound structure of a new chaotic attractor , 2002 .

[10]  Yongjian Liu,et al.  Analysis of global dynamics in an unusual 3D chaotic system , 2012 .

[11]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[12]  Hossein Aminikhah,et al.  Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives , 2016 .

[13]  H. Aminikhah,et al.  Stability analysis of Hilfer fractional differential systems , 2015 .

[14]  O. Rössler.  CONTINUOUS CHAOS—FOUR PROTOTYPE EQUATIONS , 1979 .

[15]  Guanrong Chen,et al.  Feedback anticontrol of discrete chaos , 1998 .

[16]  O. Rössler.  An equation for continuous chaos , 1976 .

[17]  Zhi-Hong Guan,et al.  Generating chaos for discrete time-delayed systems via impulsive control. , 2010, Chaos.

[18]  M. Markus,et al.  On-off intermittency and intermingledlike basins in a granular medium. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Chi K. Tse,et al.  Impulsive control and synchronization of the Lorenz systems family , 2007 .

[20]  Kwok-Wo Wong,et al.  An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion , 2013, Commun. Nonlinear Sci. Numer. Simul..

[21]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

[22]  Gang Hu,et al.  Chaos-based secure communications in a large community. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  A. Sheikhani,et al.  New identities for the Wright and the Mittag-Leffler functions using the Laplace transform , 2014 .

[24]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

[25]  W. Ditto,et al.  Controlling chaos in the brain , 1994, Nature.

[26]  Luigi Fortuna,et al.  A chaotic circuit based on Hewlett-Packard memristor. , 2012, Chaos.

[27]  Wansheng Tang,et al.  Approximate synchronization of two non-linear systems via impulsive control , 2012, J. Syst. Control. Eng..

[28]  Runzi Luo,et al.  Synchronization of uncertain fractional-order chaotic systems via a novel adaptive controller , 2017 .

[29]  H. Aminikhah,et al.  Stability Analysis of Distributed Order Fractional Chen System , 2013, TheScientificWorldJournal.

[30]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[31]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[32]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .