MEAN FIELD FLUCTUATION OF A NETWORK OF CHAOTIC ELEMENTS - REMAINING FLUCTUATION AND CORRELATION IN THE LARGE SIZE LIMIT

被引:138
作者
KANEKO, K
机构
[1] Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo, Meguro-ku, Tokyo, 153, Komaba
来源
PHYSICA D | 1992年 / 55卷 / 3-4期
关键词
D O I
10.1016/0167-2789(92)90066-V
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Fluctuation of the mean field is studied for a network of chaotic elements with the use of globally coupled maps. As the size N is increased, the variance of the mean field decreases up to a crossover size N(c) but then stays constant, where the remaining variance is roughly proportional to 1/N(c). The distribution of the mean field approaches a Gaussian form up to N(c), but keeps some deviation for N > N(c). The breakdown of the law of large numbers implies some hidden coherence among elements, confirmed by finite mutual information and Lyapunov spectra. The breakdown is also supported by the instability of the self-consistent solution for the Perron-Frobenius operator. The anomalous effect of additional noise to our system is also reported. Results from other globally coupled maps suggest that the law of large numbers is generally broken in a turbulent phase with local stretching and contraction, but is satisfied for a map with stretching only.
引用
收藏
页码:368 / 384
页数:17
相关论文
共 32 条
  • [1] ERGODIC THEORY OF AXIOM A FLOWS
    BOWEN, R
    RUELLE, D
    [J]. INVENTIONES MATHEMATICAE, 1975, 29 (03) : 181 - 202
  • [2] Chaos in a multimode solid-state laser system
    Bracikowski, C.
    Roy, Rajarshi
    [J]. CHAOS, 1991, 1 (01) : 49 - 64
  • [3] Spacetime chaos in coupled map lattices
    Bunimovich, L. A.
    Sinai, Ya G.
    [J]. NONLINEARITY, 1988, 1 (04) : 491 - 516
  • [4] Crutchfield J., 1987, DIRECTIONS CHAOS
  • [5] Eigen M, 1979, HYPERCYCLE
  • [7] HADLEY P, 1989, PHYS REV LETT, V62, P1335
  • [8] MEAN-FIELD THEORY AND CRITICAL-BEHAVIOR OF COUPLED MAP LATTICES
    HOULRIK, JM
    WEBMAN, I
    JENSEN, MH
    [J]. PHYSICAL REVIEW A, 1990, 41 (08): : 4210 - 4222
  • [9] INFORMATION THEORETICAL CHARACTERIZATION OF TURBULENCE
    IKEDA, K
    MATSUMOTO, K
    [J]. PHYSICAL REVIEW LETTERS, 1989, 62 (19) : 2265 - 2268
  • [10] GENETIC FUSION
    IKEGAMI, T
    KANEKO, K
    [J]. PHYSICAL REVIEW LETTERS, 1990, 65 (26) : 3352 - 3355