Overview: Synchronization and patterns in complex systems.

The theory of complex systems, such as neural assemblies or lattices of chaotic oscillators has generated many new problems including the synchronization or regularization of the cooperative behavior of systems consisting of chaotic elements, regular spatial patterns in "chaotic" lattices, and so on. A number of these problems were discussed at the International School in Nonlinear Science-95 (Nizhniy Novgorod, Russia). In this overview we try to formulate some of the most interesting problems that were discussed at that meeting. (c) 1996 American Institute of Physics.

[1]  Hatsuo Hayashi,et al.  Chaotic nature of bursting discharges in the Onchidium pacemaker neuron , 1992 .

[2]  G. Mpitsos,et al.  Evidence for chaos in spike trains of neurons that generate rhythmic motor patterns , 1988, Brain Research Bulletin.

[3]  S. V. Kiyashko,et al.  Domains, Domain Walls and Dislocations in Capillary Ripples , 1994 .

[4]  Tsimring.  Nested strange attractors in spatiotemporal chaotic systems. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  W. Pesch,et al.  Complex spatiotemporal convection patterns. , 1996, Chaos.

[6]  Nikolai F. Rulkov,et al.  Images of synchronized chaos: Experiments with circuits. , 1996, Chaos.

[7]  Terrence J. Sejnowski,et al.  RAPID STATE SWITCHING IN BALANCED CORTICAL NETWORK MODELS , 1995 .

[8]  Valentin Afraimovich,et al.  Dynamical description of spatial disorder , 1992 .

[9]  Steinberg,et al.  Observation of coexisting upflow and downflow hexagons in Boussinesq Rayleigh-Bénard convection. , 1996, Physical review letters.

[10]  L. Tsimring,et al.  Random pining of localized states and the birth of deterministic disorder within gradient models , 1994 .

[11]  H. Swinney,et al.  Transition from a uniform state to hexagonal and striped Turing patterns , 1991, Nature.

[12]  Makarov,et al.  Spatial chaos in a chain of coupled bistable oscillators. , 1995, Physical review letters.

[13]  Leonid L. Rubchinsky,et al.  Time-periodic spatial chaos in the complex Ginzburg-Landau equation , 1996 .

[14]  Manuel G. Velarde,et al.  Convective instability: A physicist's approach , 1977 .

[15]  Martienssen,et al.  Characterization of spatiotemporal chaos from time series. , 1993, Physical review letters.

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