2025/01/01 by Rémi Delage, Toshihiko Nakata · 1 voice · 1 citation
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Complex Systems and Time Series Analysis #Chaos control and synchronization
paper · doi:10.1063/5.0235311
openalex publication_date 2025/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
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.