Ascertaining when a basin is Wada: the merging method

TL;DR

The paper introduces a fast, efficient method to determine if a basin boundary has the Wada property by analyzing its invariance under basin merging, without needing detailed system knowledge.

Contribution

It proposes a novel merging method for testing the Wada property that is faster and requires less detailed dynamical information than previous techniques.

Findings

The merging method accurately identifies Wada boundaries.

The method is computationally more efficient than existing approaches.

It does not require detailed knowledge of the dynamical system.

Abstract

Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under the action of merging the basins. This observation allows to develop a new method to test the Wada property, which is much faster than the previous ones. Furthermore, another major advantage of the merging method is that a detailed knowledge of the dynamical system is not required.