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Scaling of Lyapunov exponents of coupled chaotic systems

  • We develop a statistical theory of the coupling sensitivity of chaos. The effect was first described by Daido [Prog. Theor. Phys. 72, 853 (1984)]; it appears as a logarithmic singularity in the Lyapunov exponent in coupled chaotic systems at very small couplings. Using a continuous-time stochastic model for the coupled systems we derive a scaling relation for the largest Lyapunov exponent. The singularity is shown to depend on the coupling and the systems' mismatch. Generalizations to the cases of asymmetrical coupling and three interacting oscillators are considered, too. The analytical results are confirmed by numerical simulations.

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Author:Rüdiger Zillmer, Volker AhlersORCiDGND, Arkadij S. Pikovskij
Document Type:Article
Year of first Publication:2000
Year of Completion:2000
Release Date:2017/03/24
Source:Physical Review / E. - 61 (2000), 1, S. 332 - 341
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik