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 [Ch. Skokos et al., Phys. Rev. Lett. 111, 064101 (2013)], we verify that chaotic dynamics is slowing down for both 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 $\mathrm{\Lambda }$ decays in time $t$ as $\mathrm{\Lambda }\propto t^{{\alpha }_{\mathrm{\Lambda }}}$, with ${\alpha }_{\mathrm{\Lambda }}$ being different from the ${\alpha }_{\mathrm{\Lambda }}=-1$ value observed in cases of regular motion. In particular, ${\alpha }_{\mathrm{\Lambda }}\approx -0.25$ (weak chaos) and ${\alpha }_{\mathrm{\Lambda }}\approx -0.3$ (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 $\mathrm{\Lambda }$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.

• Received 9 September 2018

DOI:https://doi.org/10.1103/PhysRevE.98.052229