Contrasting chaotic with stochastic dynamics via ordinal transition networks

Abstract

We introduce a representation space to contrast chaotic with stochastic dynamics. Following the complex network representation of a time series through ordinal pattern transitions, we propose to assign each system a position in a two-dimensional plane defined by the permutation entropy of the network (global network quantifier) and the minimum value of the permutation entropy of the nodes (local network quantifier). The numerical analysis of representative chaotic maps and stochastic systems shows that the proposed approach is able to distinguish linear from non-linear dynamical systems by different planar locations. Additionally, we show that this characterization is robust when observational noise is considered. Experimental applications allow us to validate the numerical findings and to conclude that this approach is useful in practical contexts.

We introduce a representation space to contrast chaotic with stochastic dynamics. Following the complex network representation of a time series through ordinal pattern transitions, we propose to assign each system a position in a two-dimensional plane defined by the permutation entropy of the network (global network quantifier) and the minimum value of the permutation entropy of the nodes (local network quantifier). The numerical analysis of representative chaotic maps and stochastic systems shows that the proposed approach is able to distinguish linear from non-linear dynamical systems by different planar locations. Additionally, we show that this characterization is robust when observational noise is considered. Experimental applications allow us to validate the numerical findings and to conclude that this approach is useful in practical contexts.