Generalized Extreme Value distribution parameters as dynamical indicators of Stability

TL;DR

This paper proposes a novel stability indicator for dynamical systems using Extreme Value statistics, offering faster computation and additional insights into attractor properties, validated on the Standard map.

Contribution

It introduces a new stability indicator based on GEV distribution parameters that outperforms existing methods in speed and provides attractor information.

Findings

Faster stability assessment than tangent map methods

Provides local stability insights through GEV parameters

Validated on Standard map dynamics

Abstract

We introduce a new dynamical indicator of stability based on the Extreme Value statistics showing that it provides an insight on the local stability properties of dynamical systems. The indicator perform faster than other based on the iteration of the tangent map since it requires only the evolution of the original systems and, in the chaotic regions, gives further information about the information dimension of the attractor. A numerical validation of the method is presented through the analysis of the motions in a Standard map.