Engineering chimera patterns in networks using heterogeneous delays

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.

7 pages,6 figures. Supplemental Material available at https://figshare.com/s/1f836f334db39dc3cd58

References in corpus (14)

• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Delays, connection topology, and synchronization of coupled chaotic maps
• Chimera states in a multilayer network of coupled and uncoupled neurons
• Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling
• Chimera states: Effects of different coupling topologies
• Clustering as a prerequisite for chimera states in globally coupled systems
• Control of amplitude chimeras by time delay in dynamical networks
• Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control
• Uncovering Randomness and Success in Society
• Optimized evolution of networks for principal eigenvector localization
• Is repulsion good for the health of Chimeras?
• Localization of multilayer networks by the optimized single-layer rewiring
• Impact of heterogeneous delays on cluster synchronization
• Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model

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• Taming Chimeras in Networks through Multiplexing Delays
• Chimera states in networks of locally and non-locally coupled SQUIDs
• Controlled Generation of Chimera States in SQUID Metasurfaces using DC Flux Gradients
• Pinning control of chimera states in systems with higher-order interactions