Mapping dynamical systems onto complex networks

TL;DR

This paper introduces a method to analyze chaotic dynamical systems by mapping them onto complex networks, revealing distinct network features that correspond to different dynamical regimes.

Contribution

It presents a novel approach to characterize chaos by translating dynamical behavior into network properties, especially focusing on higher order neighborhood metrics.

Findings

Networks differ significantly between chaotic and non-chaotic regimes

Distinct network features correlate with specific dynamical behaviors

Method successfully applied to the logistic map at chaos onset

Abstract

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent the transitions between these regions. Parameters used to quantify the properties of complex networks, including those related to higher order neighborhoods, are used in the analysis. The methodology is tested for the logistic map, focusing the onset of chaos and chaotic regimes. It is found that the corresponding networks show distinct features, which are associated to the particular type of dynamics that have generated them.