NON-TRIVIAL COLLECTIVE BEHAVIOR IN EXTENSIVELY-CHAOTIC DYNAMICAL SYSTEMS :AN UPDATE

Extensively-chaotic dynamical systems often exhibit non-trivial collective behavior: spatially-averaged quantities evolve in time, even in the infinite-size, infinite-time limit, in spite of local chaos in space and time. After a brief introduction, we give our current thoughts about the important problems related to this phenomenon. In particular, we discuss the nature of non-trivial collective behavior and the properties of the dynamical phase transitions observed at global bifurcation points between two types of collective motion.

[1]  Binder,et al.  Second-order dynamics in the collective temporal evolution of complex systems. , 1992, Physical review letters.

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

[3]  Cerdeira,et al.  Instabilities and nonstatistical behavior in globally coupled systems. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  Biswas,et al.  Local-to-global coupling in chaotic maps. , 1992, Physical review. A, Atomic, molecular, and optical physics.

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

[6]  Miller,et al.  Macroscopic equilibrium from microscopic irreversibility in a chaotic coupled-map lattice. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Herrmann,et al.  Comment on "Second-order dynamics in the collective temporal evolution of complex systems" , 1993, Physical review letters.

[8]  Hugues Chaté,et al.  Non-trivial collective behavior in coupled map lattices: a transfer operator perspective , 1997 .

[9]  Y. Pomeau.  Periodic behavior of cellular automata , 1993 .

[10]  Kaneko,et al.  Globally coupled chaos violates the law of large numbers but not the central-limit theorem. , 1990, Physical review letters.

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

[12]  Collective behaviors in a family of high-dimensional cellular automata , 1992 .

[13]  Tang,et al.  Long-range correlations in systems with coherent (quasi)periodic oscillations. , 1995, Physical review letters.

[14]  Lemaître,et al.  Cluster Expansion for Collective Behavior in Discrete-Space Dynamical Systems. , 1996, Physical review letters.

[15]  Cerdeira,et al.  Nonstatistical behavior of coupled optical systems. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[16]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[17]  H. Herrmann,et al.  On Oscillations in Cellular Automata , 1992, cond-mat/9212026.

[18]  Paul Manneville,et al.  Evidence of Collective Behaviour in Cellular Automata , 1991 .

[19]  Michael C. Mackey,et al.  Phase transitions in networks of chaotic elements with short and long range interactions , 1995 .

[20]  Henry S. Greenside,et al.  Relation between fractal dimension and spatial correlation length for extensive chaos , 1994, Nature.

[21]  Sudeshna Sinha,et al.  Order in the turbulent phase of globally coupled maps , 1993 .

[22]  Jan Hemmingsson.  A totalistic three-dimensional cellular automaton with quasiperiodic behaviour , 1992 .

[23]  Coupled map models for chaos in extended systems. , 1992, Chaos.

[24]  Peter Grassberger,et al.  Noisy collective behaviour in deterministic cellular automata , 1992 .

[25]  Coherence, chaos, and broken symmetry in classical, many-body dynamical systems. , 1987, Physical review letters.

[26]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[27]  Paul Manneville,et al.  Emergence of effective low-dimensional dynamics in the macroscopic behaviour of coupled map lattices , 1992 .

[28]  Paul Manneville,et al.  Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating , 1992 .

[29]  K. Kaneko.  Mean field fluctuation of a network of chaotic elements: Remaining fluctuation and correlation in the large size limit , 1992 .

[30]  Bennett,et al.  Stability of temporally periodic states of classical many-body systems. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[31]  Naoko Nakagawa,et al.  From collective oscillations to collective chaos in a globally coupled oscillator system , 1994 .

[32]  Naoko Nakagawa,et al.  Collective Chaos in a Population of Globally Coupled Oscillators , 1993 .

[33]  Statistical cycling in coupled map lattices. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  P. Hohenberg,et al.  Chaotic behavior of an extended system , 1989 .

[35]  Defect-mediated stability: an effective hydrodynamic theory of spatiotemporal chaos , 1994, cond-mat/9412041.