Anti-Phase Regularization of Coupled Chaotic Maps Modelling Bursting Neurons

We introduce a new class of maps that describe the chaotic activity of spiking-bursting neurons observed in neurophysiological experiments. We show that, depending on the connection (diffusively or reciprocally synaptically), coupled maps demonstrate several modes of cooperative dynamics: i) weakly correlated chaotic pulsations, ii) anti-phase quasi-regular bursting activity and iii) chaotic synchronization. Such phenomena have been observed in recent experiments with central pattern generator chaotic neurons. Taking into account the fact that the shape and the amplitude of the spikes are not important for the organisation of such cooperative dynamics, we analyzed the timing of the bursts only. We showed that the regime of anti-phase regularisation is stable against noise.