Loss of coherence in a system of globally coupled maps

O. Popovych, Yu. Maistrenko, Erik Mosekilde

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Abstract

We study the formation of symmetric (i.e., equally sized) or nearly symmetric clusters in an ensemble of the coherent state and globally coupled, identical chaotic maps. It is shown that the loss of synchronization for the emergence of subgroups of oscillators with synchronized behavior are two distinct processes, and that the type of behavior that arises after the loss of total synchronization depends sensitively on the dynamics of the individual map. For our system of globally coupled logistic maps, symmetric two-cluster formation is found to proceed through a periodic state associated with the stabilization either of an asynchronous period-2 cycle or of an asynchronous period-4 cycle. With further reduction of the coupling strength, each of the principal clustering states undergoes additional bifurcations leading to cycles of higher periodicity or to quasiperiodic and chaotic dynamics. If desynchronization of the coherent chaotic state occurs before the formation of stable clusters becomes possible, high-dimensional chaotic motion is observed in the intermediate parameter interval.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume64
Issue number2
Pages (from-to)026205
ISSN1063-651X
DOIs
Publication statusPublished - 2001

Bibliographical note

Copyright (2001) American Physical Society

Keywords

  • LOGISTIC MAPS
  • PARTIAL SYNCHRONIZATION
  • DYNAMICAL-SYSTEMS
  • TRANSVERSE INSTABILITY
  • NOISE-INDUCED SELECTION
  • CONDITIONAL LYAPUNOV EXPONENTS
  • LATTICES
  • RIDDLED BASINS
  • BLOWOUT BIFURCATIONS
  • ATTRACTORS

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