Projective Synchronization of Unidentical Chaotic Systems Based on Stability Criterion

A new method of projective synchronization of unidentical chaotic systems is proposed in this letter. This method is based on the stability criterion of linear systems. The response of two unidentical chaotic systems can synchronize up to any desired scaling factor by a suitable separation of the systems. The new method of projective synchronization is suitable not only for the three-dimensional coupled partially linear systems, but also for higher dimensional even hyperchaotic systems. The simplicity and effectiveness of the proposed method are illustrated by the Lorenz system, the four-dimensional partially linear system, the four-dimensional hyperchaotic Rosser system and Chua's circuit system as four numerical examples.

[1]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[2]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Daolin Xu,et al.  Criteria for the occurrence of projective synchronization in chaotic systems of arbitrary dimension , 2002 .

[4]  González-Miranda Jm,et al.  Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving. , 1996 .

[5]  S. Bishop,et al.  Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. , 2001, Chaos.

[6]  C. Chee,et al.  A necessary condition of projective synchronization in discrete-time systems of arbitrary dimensions , 2004 .

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

[8]  Parlitz,et al.  Encoding messages using chaotic synchronization. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Dominique M. Durand,et al.  Phase synchronization in two coupled chaotic neurons , 1999 .

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

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

[12]  Hongjie Yu,et al.  Chaotic synchronization based on stability criterion of linear systems , 2003 .

[13]  H. Agiza,et al.  Synchronization of Rossler and Chen chaotic dynamical systems using active control , 2001, Physics Letters A.

[14]  O. Rössler.  An equation for hyperchaos , 1979 .

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