The effect of coupling sensitivity of chaos is known as logarithmic singular behavior of the Lyapunov exponents of coupled chaotic systems at small values of the coupling parameter. In order to study it analytically, we use a continuous-time stochastic model which can be treated by means of the Fokker-Planck equation. One main result is that the singularity depends on the fluctuations of the finite-time Lyapunov exponents and on the mismatch between the coupled systems. We derive scaling relations for the Lyapunov exponents and give a qualitative explanation of the origin of the logarithmic singularity. The analytical predictions are compared with results of numerical calculations for different deterministic systems.

Topics
Chaotic systems, Statistical models, Lyapunov exponent, Dynamical systems, Stochastic processes
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© 2000 American Institute of Physics.
2000
American Institute of Physics
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