Mixed mode synchronization and network bursting of neurons with   post-inhibitory rebound
  This study is focused on the mechanisms of rhythmogenesis and robustness of anti-phase bursting in half-center-oscillators (HCOs) consisting of two reciprocally inhibitory coupled neurons. There is a growing body of experimental evidence that a HCO is a universal building block for larger neural networks, including central pattern generators (CPGs) controlling a variety of locomotion behaviors in spineless animals and mammals. It remains unclear how CPGs achieve the level of robustness and stability observed in nature. There has been a vastly growing consensus in the community of neurophysiologists and computational researchers that some basic structural and functional elements are likely shared by CPGs of both invertebrate and vertebrate animals. In this study we consider several configurations of HCOs including coupled endogenous bursters, tonic spiking, and quiescent neurons, that become network bursters only when coupled by fast inhibitory synapses through the mechanism of post-inhibitory-rebound (PIR). The goal is better understanding the PIR mechanism as a key component for robust anti-phase bursting in generic HCOs 
Roman Nagornov, Grigory Osipov, Maxim Komarov, Arkady Pikovsky, and   Andrey Shilnikov
nlin.CD math.DS nlin.AO