Chaos synchronization in long-range coupled map lattices

We investigate the synchronization phenomenon in 1D coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the number of maps, the coupling strength and the range of the interactions, complete chaos synchronization may be attained. The synchronization domain in the coupling parameter space can be analytically determined by means of the condition of negativity of the largest transversal Lyapunov exponent. In this Letter we use previously found analytical expressions for the synchronization frontier to analyze in detail the role of all the system parameters in the ability of the lattice to achieve complete synchronization. Analytical predictions are shown to be in accord with the outcomes of numerical experiments.

[1]  S. Nagel,et al.  SELF-ORGANIZED SHORT-TERM MEMORIES , 1996, cond-mat/9606223.

[2]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[3]  G. Rangarajan,et al.  Stability of synchronized chaos in coupled dynamical systems , 2002, nlin/0201037.

[4]  P. Gade,et al.  Synchronization and coherence in thermodynamic coupled map lattices with intermediate-range coupling. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  R. Viana,et al.  Synchronization plateaus in a lattice of coupled sine-circle maps. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Synchronization of Coupled Kicked Limit Cycle Systems , 1998 .

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

[8]  Kunihiko Kaneko,et al.  Theory and Applications of Coupled Map Lattices , 1993 .

[9]  Celia Anteneodo,et al.  Analytical results for coupled-map lattices with long-range interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Pedro G Lind,et al.  Inducing coherence in networks of bistable maps by varying the interaction range. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Yeng Chai Soh,et al.  Chaotic cryptosystem with high sensitivity to parameter mismatch , 2003 .

[12]  E. Ott,et al.  The onset of synchronization in systems of globally coupled chaotic and periodic oscillators , 2002, nlin/0205018.

[13]  K. Kaneko.  Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements , 1990 .

[14]  Celia Anteneodo,et al.  Erratum: Analytical results for coupled-map lattices with long-range interactions [Phys. Rev. E68, 045202(R) (2003)] , 2004 .

[15]  C. Beck,et al.  Thermodynamics of chaotic systems , 1993 .

[16]  Yoshiki Kuramoto,et al.  Power-law spatial correlations and the onset of individual motions in self-oscillatory media with non-local coupling , 1997 .

[17]  Mingzhou Ding,et al.  STABILITY OF SYNCHRONOUS CHAOS AND ON-OFF INTERMITTENCY IN COUPLED MAP LATTICES , 1997 .

[18]  Cerdeira,et al.  Coupled maps on trees. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[20]  Glazier,et al.  Spatially coherent states in fractally coupled map lattices. , 1995, Physical review letters.

[21]  Yoshiki Kuramoto,et al.  Multiaffine chemical turbulence , 1998 .

[22]  K. Kaneko.  Lyapunov analysis and information flow in coupled map lattices , 1986 .