使用最优传输距离与吸引子废墟复杂性的全局耦合映射聚类分析
Cluster Analysis for Globally Coupled Map using Optimal Transport Distance and Complexity of Attractor-ruin
AI总结：
该研究利用最优传输距离对全局耦合映射的轨道进行聚类分析，数值评估吸引子废墟强度，发现混沌游弋发生的部分有序相区域中吸引子废墟强度较高。
摘要：
本文展示了全局耦合映射中吸引子废墟强度的研究结果。全局耦合映射（GCM）是一种离散动力系统，这里考虑的是 logistic 映射被全局耦合的模型。吸引子废墟是指吸引子因参数变化而失稳后形成的集合，其特征由 Milnor 吸引子刻画。被称为混沌游弋的间歇现象表现为轨道在不同吸引子废墟之间转移，已在多种复杂系统中被观测到，其产生机制和统计性质受到关注。本研究从聚类角度，利用最优传输距离分析 GCM 轨道的不稳定性，并通过应用该方法对吸引子废墟的强度进行数值评估。结果发现，在被称为部分有序相且发生混沌游弋的参数区域内，各种吸引子废墟的强度较高。
英文摘要：
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.
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