Classifying basins of attraction using the basin entropy

TL;DR

This paper introduces the use of basin entropy to classify basins of attraction in nonlinear dynamical systems, revealing connections with other measures of unpredictability.

Contribution

It provides a novel framework for classifying basins of attraction using basin entropy and explores its relationship with existing unpredictability measures.

Findings

Basin entropy effectively classifies different basin types.

Connections established between basin entropy and measures like the uncertainty exponent and lacunarity.

Insights into the unpredictability of basins of attraction in nonlinear systems.

Abstract

A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to characterize the unpredictability associated to the basins of attraction, such as the uncertainty exponent, the lacunarity or other different parameters related to the Wada property.