Generalized projective synchronization of chaos: The cascade synchronization approach

The generalized projective synchronization has recently been observed in the coupled chaotic systems. In this paper, we apply the so-called “cascade synchronization approach” to this kind of synchronization, which is shown in the chaotic Lorenz system, the chaotic Rossler system, and the chaotic Chen one.

[1]  Daolin Xu,et al.  Controlled Projective Synchronization in Nonpartially-Linear Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[2]  Changpin Li,et al.  Estimating the Lyapunov exponents of discrete systems. , 2004, Chaos.

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

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

[5]  Louis M. Pecora,et al.  Cascading synchronized chaotic systems , 1993 .

[6]  Guanrong Chen,et al.  A Note on Hopf bifurcation in Chen's System , 2003, Int. J. Bifurc. Chaos.

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

[8]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

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

[10]  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.

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

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

[13]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

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

[17]  Daolin Xu,et al.  Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Xiaohua Xia,et al.  On the bound of the Lyapunov exponents for continuous systems. , 2004, Chaos.

[19]  Changpin Li,et al.  Chaos in Chen's system with a fractional order , 2004 .

[20]  Daolin Xu,et al.  Control of the formation of projective synchronisation in lower-dimensional discrete-time systems , 2003 .

[21]  Weihua Deng,et al.  Synchronization of Chaotic Fractional Chen System , 2005 .

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

[23]  Güémez,et al.  Modified method for synchronizing and cascading chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Jianping Yan,et al.  On synchronization of three chaotic systems , 2005 .

[25]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .