Imperfect traveling chimera states induced by local synaptic gradient coupling

TL;DR

This paper reports the discovery of imperfect traveling chimera states in neuronal networks with local synaptic gradient coupling, revealing new patterns and conditions for chimera emergence even with one-way local coupling.

Contribution

It introduces a novel imperfect traveling chimera pattern induced by local synaptic gradient coupling and demonstrates chimera states can occur with one-way local coupling.

Findings

Discovery of imperfect traveling chimera states.

Chimera states occur even with one-way local coupling.

Mapping of parameter space showing transitions among patterns.

Abstract

In this paper we report the occurrence of chimera patterns in a network of neuronal oscillators, which are coupled through {\it local}, synaptic {\it gradient} coupling. We discover a new chimera pattern, namely the {\it imperfect traveling chimera} where the incoherent traveling domain spreads into the coherent domain of the network. Remarkably, we also find that chimera states arise even for {\it one-way} local coupling, which is in contrast to the earlier belief that only nonlocal, global or nearest neighbor local coupling can give rise to chimera; this find further relaxes the essential connectivity requirement of getting a chimera state. We choose a network of identical bursting Hindmarsh-Rose neuronal oscillators and show that depending upon the relative strength of the synaptic and gradient coupling several chimera patterns emerge. We map all the spatiotemporal behaviors in parameter space and identify the transitions among several chimera patterns, in-phase synchronized state and global amplitude death state.