Engineering chimera patterns in networks using heterogeneous delays

TL;DR

This paper introduces a method to engineer chimera states in networks by using heterogeneous time delays, enabling control over their spatial patterns and providing a new way to identify these states.

Contribution

The study presents a novel approach to control and engineer chimera patterns in networks through the strategic use of heterogeneous delays, and introduces a spectral graph theory-based measure for their identification.

Findings

Controlled placement of incoherent regions in chimera states.

Ability to generate one-cluster or multi-cluster chimera patterns.

Introduction of a spatial inverse participation ratio for robust chimera detection.

Abstract

Symmetry breaking spatial patterns, referred to as chimera states, have recently been catapulted into the limelight due to their coexisting coherent and incoherent hybrid dynamics. Here, we present a method to engineer a chimera state by using an appropriate distribution of heterogeneous time delays on the edges of a network. The time delays in interactions, intrinsic to natural or artificial complex systems, are known to induce various modifications in spatiotemporal behaviors of the coupled dynamics on networks. Using a coupled chaotic map with the identical coupling environment, we demonstrate that control over the spatial location of the incoherent region of a chimera state in a network can be achieved by appropriately introducing time delays. This method allows for the engineering of tailor-made one cluster or multi-cluster chimera patterns. Furthermore, borrowing a measure of eigenvector localization from the spectral graph theory, we introduce a spatial inverse participation ratio, which provides a robust way for the identification of the chimera state. This report highlights the necessity to consider the heterogeneous time delays to develop applications for the chimera states in particular and understand coupled dynamical systems in general.