Cluster Analysis for Globally Coupled Map using Optimal Transport Distance and Complexity of Attractor-ruin

Abstract: In this paper, we show the results of the strength of attractorruins for a globally coupled map. The globally coupled map (GCM) is a discrete dynamical system, and here we consider a model in which the logistic map is globally coupled. An attractor-ruin is a set in which the attractor is destabilized by a change in parameters, which is characterized by a Milnor attractor. Intermittent phenomena called chaotic itinerancy, in which orbits transition between attractor-ruin, have been observed in various complex systems, and their onset mechanisms and statistical properties have attracted attention. In this study, the instability of orbits of GCM is analyzed from the perspective of clustering using the optimal transport distance, and the strength of attractor-ruins is numerically evaluated by applying this method. As a result, it was found that the strength of various attractor-ruins is high in the parameter region called the partially ordered phase, where chaotic itinerancy occurs.