Dynamics of transitions from anti-phase to multiple in-phase synchronizations in inhibitory coupled bursting neurons

Abstract

Transition from anti-phase to in-phase synchronizations in inhibitory coupled bursting neurons is very important for locomotor rhythms of animals. Here, multiple in-phase (complete), anti-phase, and phase synchronous bursting patterns are simulated in inhibitory coupled map-based model neurons with bursting patterns, and synchronization transitions between these patterns are simulated in a two-dimensional parameter space of the coupling strength and time delay. Time delay-induced transition from anti-phase to in-phase synchronous bursting behaviors matches those observed in a biological experiment on the inhibitory coupled neurons in the stomatogastric ganglion of lobster. Furthermore, bursting patterns of the in-phase (complete) synchronous behaviors can be well interpreted with the dynamic responses of an isolated single neuron to a negative square current whose action time, duration, and strength are similar to those of the inhibitory coupling current modulated by the coupling strength and time delay. The burst of the synchronous behaviors manifests the same pattern as the square negative current-induced burst of the isolated single neuron, which is acquired with the fast–slow variable dissection method. The results not only present novel nonlinear phenomenon of the time delay-induced multiple synchronous behaviors and synchronization transitions, but also provide a reasonable interpretation with the different dynamic responses of map-based bursting model neuron to an external inhibitory stimulus applied at different phases.