Collective dynamics of chaotic chemical oscillators and the law of large numbers.

Experiments on the nontrivial collective dynamics and phase synchronization of populations of nonidentical chaotic electrochemical oscillators are presented. Without added coupling no deviation from the law of large numbers is observed. Deviations do arise with weak global or short-range coupling; large, irregular, and periodic mean field oscillations occur along with (partial) phase synchronization.

[1]  L G Brunnet,et al.  Phase coherence in chaotic oscillatory media , 1998 .

[2]  J. L. Hudson,et al.  Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. , 2000, Chaos.

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

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

[5]  Dan Luss,et al.  Impact of global interactions on patterns in a simple system , 1994 .

[6]  E. Ott,et al.  Detecting phase synchronization in a chaotic laser array. , 2001, Physical review letters.

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

[8]  Eugenio Rodriguez,et al.  Studying Single-Trials of phase Synchronous Activity in the Brain , 2000, Int. J. Bifurc. Chaos.

[9]  H Sakaguchi Phase transition in globally coupled Rössler oscillators. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  H. Haken,et al.  Stochastic resonance without external periodic force. , 1993, Physical review letters.

[11]  J. L. Hudson,et al.  Phase synchronization and suppression of chaos through intermittency in forcing of an electrochemical oscillator. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Juergen Kurths,et al.  Synchronization in a population of globally coupled chaotic oscillators , 1996 .

[13]  A. Mikhailov,et al.  Breakdown of global coupling in oscillatory chemical reactions , 1993 .

[14]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

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

[16]  Paul Manneville,et al.  NON-TRIVIAL COLLECTIVE BEHAVIOR IN EXTENSIVELY-CHAOTIC DYNAMICAL SYSTEMS :AN UPDATE , 1996 .

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

[18]  Kunihiko Kaneko,et al.  Heterogeneity-induced order in globally coupled chaotic systems , 1997 .

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

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

[21]  W Wang,et al.  Clustering of arrays of chaotic chemical oscillators by feedback and forcing. , 2001, Physical review letters.

[22]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[23]  John L. Hudson,et al.  Complexity of globally coupled chaotic electrochemical oscillators , 2000 .

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

[25]  李幼升,et al.  Ph , 1989 .

[26]  Grigory V. Osipov,et al.  PHASE SYNCHRONIZATION EFFECTS IN A LATTICE OF NONIDENTICAL ROSSLER OSCILLATORS , 1997 .

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