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 Schr\"{o}dinger 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 Λ decays in time t as Λ∝tαΛ, with αΛ being different from the
αΛ=−1 value observed in cases of regular motion. In particular,
αΛ≈−0.25 (weak chaos) and αΛ≈−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 Λ
reveals the meandering of chaotic seeds inside the wave packet, which is needed
for obtaining the chaotization of the lattice's excited part.Comment: 11 pages, 10 figure