Extreme events in two dimensional disordered nonlinear lattices

TL;DR

This paper investigates the emergence and statistical properties of extreme localized events in two-dimensional disordered nonlinear lattices, revealing a transition in recurrence time distributions influenced by nonlinearity and disorder.

Contribution

It provides new insights into the statistical behavior and transition of extreme events in disordered nonlinear lattices, highlighting the influence of nonlinearity strength.

Findings

Transient extreme events are more common in weakly nonlinear regimes.

Recurrence time distribution shifts from exponential to power law with increasing disorder.

Localized structures can be both transient and persistent, with some reaching extreme magnitudes.

Abstract

Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as well as persistent localized structures, some of which have extreme magnitude. We analyze the statistics of occurrence of these extreme collective events and find that the appearance of transient extreme events is more likely in the weakly nonlinear regime. We observe a transition in the extreme events recurrence time probability from exponential, in the nonlinearity dominated regime, to power law for the disordered one.