The 0-1 test for chaos: A review

Abstract

We review here theoretical as well as practical aspects of the 0-1 test for chaos for deterministic dynamical systems. The test is designed to distinguish between regular, i.e. periodic or quasi-periodic, dynamics and chaotic dynamics. It works directly with the time series and does not require any phase space reconstruction. This makes the test suitable for the analysis of discrete maps, ordinary differential equations, delay differential equations, partial differential equations and real world time series. To illustrate the range of applicability we apply the test to examples of discrete dynamics such as the logistic map, Pomeau–Manneville intermittency maps with both summable and nonsummable autocorrelation functions, and the Hamiltonian standardmap exhibitingweak chaos. We also consider examples of continuous time dynamics such as the Lorenz-96 system and a driven and damped nonlinear Schrödinger equation. Finally, we show the applicability of the 0-1 test for time series contaminated with noise as found in real world applications.