Duffing Oscillator and Recurrence Network

Abstract

New techniques for analyzing nonlinear and complex systems continue to be developed in order to better characterize such systems. In this study, use is made of numerical series that are generated by an experimental Duffing oscillator. Time series are converted to phase spaces using the reconstruction technique. The characteristics of three signals are compared by analyzing the phase space as networks. The Euclidean distances of the interval between the points in the time series were calculated. Then, by establishing a distance threshold between the points of the network, a proximity matrix was generated using the distances that were below the threshold. Taking into account that the network clusters are delimited by a threshold, a statistical study was performed of the cluster compositions. This explored, principally, the analysis of the shortest path between two points of the network, indicating the differences between the signals and the relevance of the density of points in the phase space in these analyses.