Projective synchronization of chaotic systems with bidirectional nonlinear coupling

This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.

[1]  Wu Xiaoqun,et al.  A unified chaotic system with continuous periodic switch , 2004 .

[2]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[3]  Daolin Xu,et al.  Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems , 2005 .

[4]  Daolin Xu,et al.  Stability criterion for projective synchronization in three-dimensional chaotic systems , 2001 .

[5]  J. Rogers.  Chaos , 1876 .

[6]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[7]  Yongguang Yu,et al.  The synchronization for time-delay of linearly bidirectional coupled chaotic system , 2007 .

[8]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

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

[10]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[11]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[12]  Q. Jia.  Projective synchronization of a new hyperchaotic Lorenz system , 2007 .

[13]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[14]  Yongguang Yu,et al.  The synchronization of linearly bidirectional coupled chaotic systems , 2004 .

[15]  Hongyue Du,et al.  Function projective synchronization of different chaotic systems with uncertain parameters , 2008 .

[16]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach , 1983 .

[17]  Swarup Poria,et al.  Synchronization of generalised linearly bidirectionally coupled unified chaotic system , 2009 .

[18]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[19]  L. Chua,et al.  Generalized synchronization of chaos via linear transformations , 1999 .