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

Volker Ahlers, Rüdiger Zillmer, Arkady Pikovsky
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The behavior of the Lyapunov exponents ͑LEs͒ 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
more » ... gs. 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.
doi:10.1103/physreve.63.036213 pmid:11308747 fatcat:w2ozzmptordrhk3wgm5whzpkom