The Combined Effect of Dynamic Chemical and Electrical Synapses in Time-Delay-Induced Phase-Transition to Synchrony in Coupled Bursting Neurons

In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh-Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.