Nonlinear Dynamic Analysis and Synchronization of Four-Dimensional Lorenz-Stenflo System and Its Circuit Experimental Implementation

Recently many chaotic systems’ circuits are designed to generate phenomenon of chaos signals. The ability to synchronize chaotic circuits opens a great number of ways to use them in application signals masking. In this paper, first a new nonlinear chaotic dynamical system had be design, analyze and build circuit. Second, using GYC, partial region stability theory is applied to adaptive control for two identical chaotic systems with uncertain parameters. The results of numerical simulation are performed to verify examples of the proposed nonlinear controllers.

[1]  Ahmed M. Soliman,et al.  MOS realization of the double-scroll-like chaotic equation , 2003 .

[2]  Yongjian Liu,et al.  Circuit implementation and finite-time synchronization of the 4D Rabinovich hyperchaotic system , 2011, Nonlinear Dynamics.

[3]  Damei Li,et al.  Bounds of the hyper-chaotic Lorenz–Stenflo system , 2010 .

[4]  Julien Clinton Sprott,et al.  Precision measurements of a simple chaotic circuit , 2004 .

[5]  Guanrong Chen,et al.  A chaotic system with only one stable equilibrium , 2011, 1101.4067.

[6]  Lennart Stenflo,et al.  Generalized Lorenz equations for acoustic-gravity waves in the atmosphere , 1996 .

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

[8]  Neil Genzlinger.  A. and Q , 2006 .

[9]  H. Santos,et al.  Electron Transmission through Graphene Bilayer Flakes , 2012 .

[10]  W. Xiang.  EQUILIBRIUM POINTS AND BIFURCATION CONTROL FOR LORENZ-STENFLO SYSTEM , 2009 .

[11]  Zhengguo Li,et al.  Switched and impulsive systems , 2005 .

[12]  Ali Abooee,et al.  Analysis and circuitry realization of a novel three-dimensional chaotic system , 2013, Commun. Nonlinear Sci. Numer. Simul..

[13]  Zheng-Ming Ge,et al.  Three Asymptotical Stability Theorems on Partial Region with Applications , 1998 .

[14]  Dusan Kocur,et al.  CHUA'S CIRCUIT IN SPREAD SPECTRUM COMMUNICATION SYSTEMS , 2002 .

[15]  J. Yorke,et al.  The liapunov dimension of strange attractors , 1983 .

[16]  W. Marsden.  I and J , 2012 .

[17]  Xiaofeng Liao,et al.  Two fuzzy control schemes for Lorenz-Stenflo chaotic system , 2012 .

[18]  Z. Ge,et al.  The generalized synchronization of a Quantum-CNN chaotic oscillator with different order systems , 2008 .

[19]  Paulo C. Rech,et al.  Regular and Chaotic Dynamics of the Lorenz-Stenflo System , 2010, Int. J. Bifurc. Chaos.

[20]  Ljupco Kocarev,et al.  Intelligent Computing Based on Chaos , 2009 .