Directed recurrence networks for the analysis of nonlinear and complex dynamical systems.

Abstract

Complex network approaches have been emerging as an analysis tool for dynamical systems. Different reconstruction methods from time series have been shown to reveal complicated behaviors that can be quantified from the network's topology. Directed recurrence networks have recently been suggested as one such method, complementing the already successful recurrence networks and expanding the applications of recurrence analysis. We investigate here their performance for the analysis of nonlinear and complex dynamical systems. It is shown that there is a strong parallel with previous Markov chain approximations of the transfer operator, as well as a few differences explained by their structure. Notably, the spectral analysis provides crucial information on the dynamics of the system, such as its complexity or dynamical patterns and their stability. Possible advantages of the directed recurrence network approach include the preserved data resolution and well defined recurrence threshold.