On the Implementation of the 0-1 Test for Chaos

TL;DR

This paper improves the implementation of the 0-1 test for chaos by enhancing its sensitivity and providing practical guidance, supported by theoretical insights and empirical examples.

Contribution

The paper introduces a new formulation of the 0-1 test that significantly increases its sensitivity and offers practical implementation strategies.

Findings

Enhanced sensitivity of the 0-1 test for chaos.

Practical implementation guidelines provided.

Illustrative examples demonstrating improvements.

Abstract

In this paper we address practical aspects of the implementation of the 0-1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method to distill a binary quantity from the power spectrum. The implementation is guided by recent results from the theoretical justification of the test as well as by exploring better statistical methods to determine the binary quantities. We give several examples to illustrate the improvement.