A New Test for Chaos

TL;DR

This paper introduces a simple, dimension-independent 0-1 test for chaos that determines whether a deterministic system is chaotic without requiring the equations or Lyapunov exponents.

Contribution

It presents a novel 0-1 test for chaos that is easy to implement, works for both continuous and discrete systems, and does not depend on the system's dimension or known equations.

Findings

The test accurately distinguishes chaotic from nonchaotic systems.

It performs well on differential equations, partial differential equations, and maps.

The method is simple and does not require Lyapunov exponent calculation.

Abstract

We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos (the output is a 0 signifying nonchaotic or a 1 signifying chaotic) and is independent of the dimension of the dynamical system. Moreover, the underlying equations need not be known. The test works equally well for continuous and discrete time. We give examples for an ordinary differential equation, a partial differential equation and for a map.