Lyapunov exponents in disordered chaotic systems: Avoided crossing and level statistics - art. no. 036213

The behavior of the Lyapunov exponents (LEs) of a disordered system consist ing of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, q ualitatively similar to the behavior of energy levels in quantum chaos. Rec ent results for the coupling dependence of the LEs of two coupled chaotic s ystems are used to explain the phenomenon and to derive an approximate expr ession for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small val ues. The results an interpreted in terms of the random matrix theory.