Identification of single- and double-well coherence-incoherence patterns by the binary distance matrix

TL;DR

This paper introduces an extended eigenvalue decomposition method to distinguish between single- and double-well coherence-incoherence patterns in complex dynamical networks, enhancing pattern identification in coupled systems.

Contribution

The work develops a novel eigenvalue-based approach to classify coherence-incoherence patterns, including single- and double-well states, in nonlocally coupled dynamical systems.

Findings

The method successfully identifies four types of patterns in coupled circuits and maps.

Adding a central node influences the prevalence of single-well states.

Attraction basin boundaries exhibit fractal and riddled structures.

Abstract

The study of chimera states or, more generally, coherence-incoherence patterns has led to the development of several tools for their identification and characterization. In this work, we extend the eigenvalue decomposition method to distinguish between single-well and double-well patterns. By applying our method, we are able to identify the following four types of dynamical patterns in a ring of nonlocally coupled Chua circuits and nonlocally coupled cubic maps: single-well cluster, single-well coherence-incoherence pattern, double-well cluster, and double-well coherence-incoherence. In a ring-star network of Chua circuits, we investigate the influence of adding a central node on the spatio-temporal patterns. Our results show that increasing the coupling with the central node favors the occurrence of single-well coherence-incoherence states. We observe that the boundaries of the attraction basins resemble fractal and riddled structures