Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound

•We study anti-phase bursting in half-center-oscillators with post-inhibitory rebound.•We consider several configurations of HCOs.•In all configurations PIR leads to robust anti-phase bursting regime.

We study an array of activity rhythms generated by a half-center oscillator (HCO), represented by a pair of reciprocally coupled neurons with post-inhibitory rebounds (PIR). Such coupling-induced bursting possesses two time scales, one for fast spiking and another for slow quiescent periods, is shown to exhibit an array of synchronization properties. We discuss several HCO configurations constituted by two endogenous bursters, by tonic-spiking and quiescent neurons, as well as mixed-mode configurations composed of neurons of different type. We demonstrate that burst synchronization can be accompanied by complex, often chaotic, interactions of fast spikes within synchronized bursts.