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

René Mikkelsen, Martin van Hecke, and Tomas Bohr
Phys. Rev. E 67, 046207 – Published 14 April 2003
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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.

  • Received 8 July 2002

DOI:https://doi.org/10.1103/PhysRevE.67.046207

©2003 American Physical Society

Authors & Affiliations

René Mikkelsen1,2, Martin van Hecke3, and Tomas Bohr4

  • 1Center for Chaos and Turbulence Studies, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
  • 2Department of Applied Physics and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
  • 3Kamerlingh Onnes Laboratory, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
  • 4Department of Physics, The Danish Technical University, DK-2800 Kgs. Lyngby, Denmark

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Vol. 67, Iss. 4 — April 2003

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