Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices

R. Mikkelsen, M. van Hecke, Tomas Bohr

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Abstract

We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany-Kinzel cellular automaton [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence that "solitons" can change the nature of the transition: for short soliton lifetimes it is of second order, while for longer but finite lifetimes, it is more reminiscent of a first-order transition. In the second-order regime, the deterministic model behaves like directed percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany-Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second- to first-order behavior due to the solitons, both in a mean-field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave like stochastic models; but it is hard to know precisely which degrees of freedom need to be included in such description.
Original languageEnglish
JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume67
Issue number4
Pages (from-to)046207
ISSN1063-651X
DOIs
Publication statusPublished - 2003

Bibliographical note

Copyright (2003) American Physical Society

Keywords

  • SYSTEMS
  • UNIVERSALITY
  • FIELD-THEORY
  • RAYLEIGH-BENARD CONVECTION
  • SPATIO-TEMPORAL INTERMITTENCY
  • CRITICAL-BEHAVIOR
  • ABSORBING STATES
  • PHASE-TRANSITIONS
  • DIRECTED PERCOLATION
  • KURAMOTO-SIVASHINSKY EQUATION;

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