Stochastic Approach to Lyapunov Exponents in Coupled Chaotic Systems
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.
KeywordsLyapunov Exponent Chaotic System Large Lyapunov Exponent Logarithmic Singularity Small Coupling
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