Complex Networks Approach for Dynamical Characterization of Nonlinear Systems

Abstract

Bifurcation diagrams and Lyapunov exponents are the main tools for dynamical systems characterization. However, they are often computationally expensive and complex to calculate. We present two approaches for dynamical characterization of nonlinear systems via the generation of an undirected complex network that is built from their time series. Periodic windows and chaos can be detected by analyzing network statistics like average degree, density and betweenness centrality. Results are assessed in two discrete time nonlinear maps.