Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering

TL;DR

This paper presents a novel methodology combining entropy measures and clustering algorithms to analyze chaotic itinerancy in dynamical systems, demonstrated on coupled logistic maps, revealing quasi-stable states and transition dynamics.

Contribution

The paper introduces a new approach using entropy and clustering to identify and analyze chaotic itinerancy, providing a systematic way to characterize complex transition behaviors.

Findings

Successfully identified quasi-stable states and transition phases in GCM

Demonstrated the method's effectiveness across various parameters

Reproduced known chaotic itinerancy phenomena algorithmically

Abstract

We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasi-stable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. Our approach then focuses on examining the chaotic itinerancy dynamics through the characterization of residence times within these states and chaotic transitions between them with the help of some statistical tests. We demonstrate the effectiveness of these methods on the system of globally coupled logistic maps (GCM), a well-known model exhibiting chaotic itinerancy. In particular, we conduct comprehensive computations for a large number of parameters in the GCM system and algorithmically identify itinerant dynamics observed previously by Kaneko in numerical simulations as coherent and intermittent phases.