Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method

Implementing the Generalized Alignment Index (GALI) method of chaos detection we investigate dynamical behavior nonlinear disordered Klein-Gordon lattice chain in one spatial dimension. By performing extensive numerical simulations single site and mode initial excitations, for several realizations different disorder strengths, determine probability to observe chaotic as system is approaching its linear limit, i.e. when total energy, which plays role system's nonlinearity strength, decreases. We find that percentage cases diminishes energy decreases leading exclusively regular motion on multidimensional tori. also discriminate between localized spreading chaos, with former dominating dynamics lower values. In addition, our results show excitations lead more behaviors larger energies compared excitations. Furthermore, demonstrate how GALI can be efficiently used a characteristic chaoticity time scale strong enough nonlinearites delocalization both so-called `weak' `strong chaos' regimes.