Devaney's chaos on recurrence plots

Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036209. doi: 10.1103/PhysRevE.82.036209. Epub 2010 Sep 23.

Abstract

Although the definition of deterministic chaos in the sense of Devaney is often employed for investigating dynamical systems, it has been rarely used for identifying deterministic chaos from time series. In this paper, we develop a set of methods that infers whether a given time series is consistent with deterministic chaos in the sense of Devaney or not. We define weaker notions of the three properties of Devaney's chaos which can be checked using a given time series of a finite length. We apply these methods for artificial and real data.