Remarks on Chaos Synchronizability and Synchronization

Synchronous behavior signifies that two or more systems operate or occur at the same time and space. Then, the synchronization problem is to induce the synchronous behavior in two or more dynamical systems. Thus, as a consequence, the synchronizability is defined as the property of dynamical systems such that the synchronous behavior can be induced on two or more dynamical systems. Such a problem can be understood as the interconnection of two or more chaotic systems in such manner that they behave in synchronous way. The synchronization can be performed by feedforward or feedback interconnections [1], [2]. In this sense synchronization problem is a control one; since synchronizability is related to the intrinsic properties of nonlinear systems to be synchronized, and such properties can be studied by exploiting the control theory concepts; controllability and observability.

[1]  Ljupco Kocarev,et al.  General approach for chaotic synchronization with applications to communication. , 1995, Physical review letters.

[2]  Ricardo Femat,et al.  Synchronization of a class of strictly different chaotic oscillators , 1997 .

[3]  R. Femat,et al.  On the chaos synchronization phenomena , 1999 .

[4]  Firdaus E. Udwadia,et al.  Some global properties of a pair of coupled maps: quasi-symmetry, periodicity, and synchronicity , 1998 .

[5]  Maciej Ogorzalek,et al.  Taming chaos. II. Control , 1993 .

[6]  Frank Pasemann,et al.  Synchronized chaos and other coherent states for two coupled neurons , 1999 .

[7]  Thomas Kailath,et al.  Linear Systems , 1980 .

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

[9]  Ljupco Kocarev,et al.  A unifying definition of synchronization for dynamical systems. , 1998, Chaos.

[10]  A. Isidori.  Nonlinear Control Systems , 1985 .

[11]  Pérez,et al.  Extracting messages masked by chaos. , 1995, Physical review letters.

[12]  P. Buono.  Models of central pattern generators for quadruped locomotion II. Secondary gaits , 2001 .

[13]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[14]  Krešimir Josić,et al.  Synchronization of chaotic systems and invariant manifolds , 2000 .

[15]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[16]  Ljupco Kocarev,et al.  Lie Derivatives and Dynamical Systems , 1998 .

[17]  S Boccaletti,et al.  Unifying framework for synchronization of coupled dynamical systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Gualberto Solís-Perales,et al.  A chaos-based communication scheme via robust asymptotic feedback , 2001 .

[19]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

[20]  Choy Heng Lai,et al.  On the synchronization of different chaotic oscillators , 2000 .

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

[22]  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.

[23]  E. Mosekilde,et al.  Synchronization phenomena in nephron-nephron interaction. , 2001, Chaos.

[24]  M. Golubitsky,et al.  Models of central pattern generators for quadruped locomotion II. Secondary gaits , 2001, Journal of mathematical biology.

[25]  Chai Wah Wu,et al.  A Simple Way to Synchronize Chaotic Systems with Applications to , 1993 .

[26]  R. Femat,et al.  Synchronization of chaotic systems with different order. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  R Femat,et al.  Complete synchronizability of chaotic systems: a geometric approach. , 2003, Chaos.