Effects of autapse on the chimera state in a Hindmarsh-Rose neuronal network

Abstract

Autapse is introduced as a self-feedback connection that connects the dendrites and axons of the same neuron. Previous studies have revealed that the existence of the autapse can influence the synchronized behaviours of the coupled neurons. In this paper, the chimera state is studied in the presence of autaptic connections. To this aim, a regular network of Hindmarsh-Rose neurons with electrical synapses and autapses is considered. The neurons' collective behaviour and firing patterns are investigated by varying the coupling and the autapse parameters. The results show that for short autaptic time delays, the chimera's occurrence domain is shifted towards lower autapse gains by increasing the coupling strength. On the other hand, the coupling strength has less effect for more extended time delays, and the chimera's domain is only dependent on the autapse gain. However, when the coupling strength grows too large, the time delay loses its effect. Consequently, a desirable dynamical state can be attained by regulating the coupling strength, coupling range, autapse time delay and autapse gain.