Chimera states in complex networks: interplay of fractal topology and delay

Abstract

Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of existence of coherent travelling waves. We demonstrate that by varying the time delay one can deliberately stabilize desired spatio-temporal patterns in the system.

arXiv admin note: text overlap with arXiv:1603.00171

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• Three-dimensional chimera patterns in networks of spiking neuron oscillators
• Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature
• Delay-induced chimeras in neural networks with fractal topology
• Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators
• Chimera states in networks of logistic maps with hierarchical connectivities
• Itinerant chimeras in an adaptive network of pulse-coupled oscillators
• Delay engineered solitary states in complex networks
• Transition from chimera/solitary states to traveling waves
• Synchronization scenarios in three-layer networks with a hub
• Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation
• Robust universal approach to identify travelling chimeras and synchronized clusters in spiking networks
• Chimera states in neural networks and power systems
• Dynamical heterogeneity and universality of power-grids
• Chimera states in networks of locally and non-locally coupled SQUIDs
• Taming Chimeras in Networks through Multiplexing Delays