Order in the turbulent phase of globally coupled maps

Abstract The broad peaks seen in the power spectra of the mean field in a globally coupled map system indicate a subtle coherence between the elements, even in the “turbulent” phase. These peaks are investigated in detail with respect to the number of elements coupled, nonlinearity and global coupling strengths. We find that this roughly periodic behavior also appears in the probability distribution of the mapping, which is therefore not invariant. We also find that these peaks are determined by two distinct components: effective renormalization of the nonlinearity parameter in the local mappings, and the strength of the mean field interaction term. Finally, we demonstrate the influence of background noise on the peaks, which is quite counterintuitive, as they become sharper with increase in strength of the noise, up to a certain critical noise strength.

[1]  Santucci,et al.  Stochastic resonance in bistable systems. , 1989, Physical review letters.

[2]  Kaneko.  Chaotic but regular posi-nega switch among coded attractors by cluster-size variation. , 1989, Physical review letters.

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

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

[5]  B. Hao,et al.  Directions in chaos , 1987 .

[6]  Hadley,et al.  Attractor crowding in oscillator arrays. , 1989, Physical review letters.

[7]  H. Daido,et al.  Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators , 1990 .

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

[9]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[10]  Fabio Marchesoni,et al.  Extraction of periodic signals from a noise background , 1989 .

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

[12]  Richard V. Solé,et al.  Order and chaos in a 2D Lotka-Volterra coupled map lattice , 1991 .

[13]  Y. Kuramoto,et al.  Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities , 1987 .

[14]  Mode locking in an infinite set of coupled circle maps. , 1987, Physical review. A, General physics.

[15]  S. Strogatz,et al.  Stability of incoherence in a population of coupled oscillators , 1991 .