Abstract
Spectral statistics of the Lyapunov exponents computed for coupled map networks bear strong signatures of different phases emergent from the spatiotemporal dynamics. We find that the distributions of gaps in the Lyapunov spectrum for the chaotic and the synchronized phases show Poisson and GOE statistics, respectively, in agreement with the universal predictions of the random matrix theory. The presence of quenched disorder in coupled map networks generates a non-trivial chaotic Griffiths phase for intermediate coupling strengths. The Lyapunov spectral statistics obtained for the chaotic Griffiths phase show strong suppression of gaps and the Lyapunov vectors indicate a unique intermittent dynamical localization.
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