# The saddle-straddle method to test for Wada basins

## TL;DR

The paper introduces the saddle-straddle method, a new technique to identify Wada basins in dynamical systems by analyzing the chaotic saddle in the boundary regions, confirming the Wada property through its invariance across basin combinations.

## Contribution

A novel saddle-straddle algorithm for detecting Wada basins by computing the chaotic saddle in the boundary of attractors.

## Key findings

- The method successfully identifies Wada basins in dynamical systems.
- The chaotic saddle is consistent across all basin combinations.
- The approach provides a practical way to verify the Wada property.

## Abstract

First conceived as a topological construction, Wada basins abound in dynamical systems. Basins of attraction showing the Wada property possess the particular feature that any small perturbation of an initial condition lying on the boundary can lead the system to any of its possible outcomes. The saddle-straddle method, described here, is a new method to identify the Wada property in a dynamical system based on the computation of its chaotic saddle in the fractalized phase space. It consists of finding the chaotic saddle embedded in the boundary between the basin of one attractor and the remaining basins of attraction by using the saddle-straddle algorithm. The simple observation that the chaotic saddle is the same for all the combinations of basins is sufficient to prove that the boundary has the Wada property.