Multiscale interaction promotes chimera states in complex networks

Abstract

We report emergence of chimera states in a multiscale network that defines a network of interconnected networks, a network of a global ring of nodes whose each node, in turn, is a member of an individual subnetwork of another ring of nodes. We reveal a variety of spatiotemporal dynamics which ensues in such complex networks by varying the inner topology of the nonlocally coupled subnetworks from local to nonlocal coupling. We find that an increment in the local connectivity of the subnetworks enhances the span of the chimera region in parameter space. We consider the Kuramoto–Sakaguchi phase model to represent each node of the network and our numerical findings show that the topology of the subnetworks greatly influences the emergence of chimera states in the global ring. We also perform an analytical study on the phase oscillator based network using the Ott–Antonsen approach, and the analytical results are found to be consistent with the numerical outcomes. Furthermore, due to high relevance of the proposed network architecture to the human brain, we consider a more realistic network of Hindmarsh–Rose neuron model and reveal a similar phenomenon when the neurons in each of the subnetworks communicate via chemical synapses while information among the subnetworks passes through gap junctions.