Intermittent cluster synchronization in a unidirectional ring of bursting neurons

We report a new mechanism through which extreme events with a dragon-king-like distribution emerge in a network of unidirectional ring of Hindmarsh-Rose bursting neurons interacting through chemical synapses. We establish and substantiate the fact that depending on the choice of initial conditions, the neurons are divided into different clusters. These clusters transit from a phase-locked state (antiphase) to phase synchronized regime with increasing value of the coupling strength. Before attaining phase synchronization, there exist some regions of the coupling strength where these clusters are phase synchronized intermittently. During such intermittent phase synchronization, extreme events originate in the mean field of the membrane potential. This mechanism, which we name as intermittent cluster synchronization, is proposed as the new precursor for the generation of emergent extreme events in this system. These results are also true for diffusive coupling (gap junctions). The distribution of the local maxima of the collective observable shows a long-tailed non-Gaussian while the interevent interval follows the Weibull distribution. The goodness of fit is corroborated using probability-probability plot and quantile-quantile plot. This intermittent phase synchronization becomes rarer and rarer with an increase in the number of clusters of initial conditions.