Identifying Time Delay-induced Multiple Synchronous Behaviours in Inhibitory Coupled Bursting Neurons with Nonlinear Dynamics of Single Neuron

Time delay-induced multiple synchronous behaviors are simulated in inhibitory coupled bursting neurons when time delay is larger than the period of the bursting, which can be well interpreted with dynamics of single neuron combined with inhibitory coupling current. The bursting pattern of uncoupled neuron can change to multiple different firing patterns when receiving negative stimulus at suitable phase to form the multiple patterns of synchronous bursting appearing at different time delay. The synchronization is dependent on the stable characteristics of the quiescent state corresponding to the stable node of the fast subsystem, wherein long lasting inhibitory coupling current is conductive to achieve synchronization. This is the reason that inhibitory coupling current modulated by time delay can induce multiple synchronous behaviors.