Transcritical loss of synchronization in coupled chaotic systems

Abstract The synchronization transition is described for a system of two asymmetrically coupled chaotic oscillators. Such a system can represent the two-cluster state in a large ensemble of globally coupled oscillators. It is shown that the transition can be typically mediated by a transcritical transversal bifurcation. The latter has a hard brunch that dominates the global dynamics, so that the synchronization transition is normally hard. For a particular example of coupled logistic maps a diversity of transition scenaria includes both local and global riddling. In the case of small non-identity of the interacting systems the riddling is shown to turn into an exterior or interior crisis.

[1]  Kunihiko Kaneko,et al.  Globally coupled circle maps , 1991 .

[2]  Grebogi,et al.  Riddling Bifurcation in Chaotic Dynamical Systems. , 1996, Physical review letters.

[3]  G. Iooss,et al.  Elementary stability and bifurcation theory , 1980 .

[4]  Erik Mosekilde,et al.  Role of the Absorbing Area in Chaotic Synchronization , 1998 .

[5]  Hadley,et al.  Phase locking of Josephson-junction series arrays. , 1988, Physical review. B, Condensed matter.

[6]  Roy,et al.  Observation of antiphase states in a multimode laser. , 1990, Physical review letters.

[7]  Krishnamurthy Murali,et al.  Efficient signal transmission by synchronization through compound chaotic signal , 1997 .

[8]  E. Mosekilde,et al.  TRANSVERSE INSTABILITY AND RIDDLED BASINS IN A SYSTEM OF TWO COUPLED LOGISTIC MAPS , 1998 .

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

[10]  Arkady Pikovsky,et al.  On the interaction of strange attractors , 1984 .

[11]  Christian Mira,et al.  Chaotic Dynamics in Two-Dimensional Noninvertible Maps , 1996 .

[12]  Roy,et al.  Experimental synchronization of chaotic lasers. , 1994, Physical review letters.

[13]  Sompolinsky,et al.  Cooperative dynamics in visual processing. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[14]  S. Boccaletti,et al.  ADAPTIVE SYNCHRONIZATION OF CHAOS FOR SECURE COMMUNICATION , 1997 .

[15]  Kurths,et al.  Do globally coupled maps really violate the law of large numbers? , 1994, Physical review letters.

[16]  Martin,et al.  New method for determining the largest Liapunov exponent of simple nonlinear systems. , 1986, Physical review. A, General physics.

[17]  O. Popovych,et al.  Desynchronization of chaos in coupled logistic maps. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Ott,et al.  Transitions to Bubbling of Chaotic Systems. , 1996, Physical review letters.

[19]  Jinghua Xiao,et al.  Synchronization of spatiotemporal chaos and its applications , 1997 .

[20]  Falcioni,et al.  Broken ergodicity and glassy behavior in a deterministic chaotic map. , 1996, Physical review letters.

[21]  A. Cenys,et al.  On-off intermittency in chaotic synchronization experiment , 1996 .

[22]  Kunihiko Kaneko,et al.  On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection , 1998, chao-dyn/9802016.

[23]  Louis M. Pecora,et al.  Fundamentals of synchronization in chaotic systems, concepts, and applications. , 1997, Chaos.