Controlling phase synchrony in the mean field coupled Hindmarsh–Rose neurons

Abstract

The phase synchronization in a network of mean field coupled Hindmarsh–Rose neurons and the control of phase synchrony by an external input has been analyzed in this work. The analysis of interspike interval, with varying coupling strength, reveals the dynamical change induced in each neuron in the network. The bursting phase lines depict that mean field coupling induces phase synchrony in excitatory mode and desynchrony in inhibitory mode. The coefficient of variability, in spatial and temporal domain, signifies the deviations in firing times of neurons, in a collective manner. The Kuramoto order parameter quantifies the intermittent and complete phase synchrony, induced by excitatory mean field coupling. The capability of external input, in the form of spikes, to control the intermittent and complete phase synchrony has been analyzed. The coefficient of variability and Kuramoto order parameter has been studied by varying the amplitude, pulse width and frequency of the input. The studies have shown that high-frequency spike input, with optimum amplitude and pulse width, has high desynchronizing ability, which is substantiated by the parameter space analysis. The control of synchrony in the network of neurons may find application in rectifying neural disorders.