Generalized Extreme Value distribution parameters as dynamical indicators of Stability

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.

References in corpus (3)

• Extremal Index, Hitting Time Statistics and periodicity
• Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
• Analysis of Round Off Errors with Reversibility Test as a Dynamical Indicator

Cited by in corpus (10)

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• Extreme value statistics for dynamical systems with noise
• A novel concept of fractal dimension in deterministic and stochastic Lorenz-63 systems
• Disentangling regular and chaotic motion in the standard map using complex network analysis of recurrences in phase space
• Robust estimate of dynamo thresholds in the von Kármán sodium experiment using the Extreme Value Theory
• Evidence for crisis-induced intermittency during geomagnetic superchron transitions
• Mixing properties in the advection of passive tracers via recurrences and extreme value theory