# 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.

## Key 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.