Persistent clusters in lattices of coupled nonidentical chaotic systems

被引:105
作者
Belykh, I [1 ]
Belykh, V
Nevidin, K
Hasler, M
机构
[1] Swiss Fed Inst Technol, Nonlinear Syst Lab, CH-1015 Lausanne, Switzerland
[2] Volga State Acad, Dept Math, Nizhnii Novgorod 603600, Russia
关键词
D O I
10.1063/1.1514202
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Two-dimensional (2D) lattices of diffusively coupled chaotic oscillators are studied. In previous work, it was shown that various cluster synchronization regimes exist when the oscillators are identical. Here, analytical and numerical studies allow us to conclude that these cluster synchronization regimes persist when the chaotic oscillators have slightly different parameters. In the analytical approach, the stability of almost-perfect synchronization regimes is proved via the Lyapunov function method for a wide class of systems, and the synchronization error is estimated. Examples include a 2D lattice of nonidentical Lorenz systems with scalar diffusive coupling. In the numerical study, it is shown that in lattices of Lorenz and Rossler systems the cluster synchronization regimes are stable and robust against up to 10%-15% parameter mismatch and against small noise. (C) 2003 American Institute of Physics.
引用
收藏
页码:165 / 178
页数:14
相关论文
共 56 条
  • [1] Generalized synchronization of chaos: The auxiliary system approach
    Abarbanel, HDI
    Rulkov, NF
    Sushchik, MM
    [J]. PHYSICAL REVIEW E, 1996, 53 (05) : 4528 - 4535
  • [2] Synchronization in lattices of coupled oscillators
    Afraimovich, VS
    Chow, SN
    Hale, JK
    [J]. PHYSICA D, 1997, 103 (1-4): : 442 - 451
  • [3] Synchronization in lattices of coupled oscillators with Neumann/periodic boundary conditions
    Afraimovich, VS
    Lin, WW
    [J]. DYNAMICS AND STABILITY OF SYSTEMS, 1998, 13 (03): : 237 - 264
  • [4] AFRAIMOVICH VS, 1996, IZV VYSSH UCHEBN ZAV, V29, P795
  • [5] RIDDLED BASINS
    Alexander, J. C.
    Yorke, James A.
    You, Zhiping
    Kan, I.
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1992, 2 (04): : 795 - 813
  • [6] Intermingled basins for the triangle map
    Alexander, JC
    Hunt, BR
    Kan, I
    Yorke, JA
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1996, 16 : 651 - 662
  • [7] BUBBLING OF ATTRACTORS AND SYNCHRONIZATION OF CHAOTIC OSCILLATORS
    ASHWIN, P
    BUESCU, J
    STEWART, I
    [J]. PHYSICS LETTERS A, 1994, 193 (02) : 126 - 139
  • [8] The Lorenz-Fermi-Pasta-Ulam experiment
    Balmforth, NJ
    Pasquero, C
    Provenzale, A
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2000, 138 (1-2) : 1 - 43
  • [9] One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
    Belykh, VN
    Mosekilde, E
    [J]. PHYSICAL REVIEW E, 1996, 54 (04): : 3196 - 3203
  • [10] Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems
    Belykh, VN
    Belykh, IV
    Hasler, M
    [J]. PHYSICAL REVIEW E, 2000, 62 (05): : 6332 - 6345