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Lyapunov exponents in disordered chaotic systems : avoided crossing and level statistics

  • The behavior of the Lyapunov exponents (LEs) of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, qualitatively similar to the behavior of energy levels in quantum chaos. Recent results for the coupling dependence of the LEs of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small values. The results are interpreted in terms of the random matrix theory.

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Author:Volker AhlersORCiDGND, Rüdiger Zillmer, Arkadij S. Pikovskij
Document Type:Article
Year of first Publication:2001
Year of Completion:2001
Release Date:2017/03/24
Source:Physical Review / E. - 63 (2001), 036213
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik