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Stochastic Approach to Lyapunov Exponents in Coupled Chaotic Systems

  • Rüdiger Zillmer
  • Volker Ahlers
  • Arkady Pikovsky
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 557)

Abstract

We use linear stochastic Langevin equations to describe the Lyapunov exponents in coupled chaotic systems. The largest Lyapunov exponent is calculated analytically, using the stationary solution of the Fokker-Planck equation. For small couplings we reproduce the singularity which was first described by Daido as the effect of coupling sensitivity of chaos. The singularity is shown to depend on the coupling and the systems’ mismatch. The analytical results are confirmed by numerical simulations.

Keywords

Lyapunov Exponent Chaotic System Large Lyapunov Exponent Logarithmic Singularity Small Coupling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Rüdiger Zillmer
    • 1
  • Volker Ahlers
    • 1
  • Arkady Pikovsky
    • 1
  1. 1.Department of PhysicsUniversity of PotsdamPotsdamGermany

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