Phase switching in Hindmarsh-Rose relay neurons

A system of Hindmarsh-Rose relay neurons with time delay coupling is considered in which the relay (central) neuron has an additional feedback term that represents the interaction activity with a local environment. The strength of environmental coupling with the central neuron plays an important role in inducing synchronization and de-synchronization between the outer neurons. The strength of feedback developed from the environmental coupling has created a gradual quenching in the oscillations of the central neuron. At a higher feedback coupling strength, oscillation of the central neuron is suppressed drastically and a transition from a regime of synchronization to out-of-phase synchronization take place between the oscillations of the two outer neurons.