Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

Abstract

We numerically investigate the characteristics of chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schrödinger equation model. Completing previous investigations \cite{SGF13} we verify that chaotic dynamics is slowing down both for the so-called `weak' and `strong chaos' dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $\Lambda$ decays in time $t$ as $\Lambda \propto t^{{\alpha }_{\Lambda }}$, with ${\alpha }_{\Lambda }$ being different from the ${\alpha }_{\Lambda }=-1$ value observed in cases of regular motion. In particular, ${\alpha }_{\Lambda }\approx -0.25$ (weak chaos) and ${\alpha }_{\Lambda }\approx -0.3$ (strong chaos) for both models, indicating the dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $\Lambda$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.

11 pages, 10 figures

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