Extreme events in locally coupled bursting neurons

We report a new mechanism through which extreme events with a dragon king-like distribution emerge in a network of locally coupled Hindmarsh-Rose bursting neurons. We establish and substantiate the fact that depending on the choice of initial conditions, the neurons in the network are divided into clusters and whenever these clusters are phase synchronized intermittently, extreme events originate in the collective observable. This mechanism, which we name as intermittent cluster synchronization is proposed as the new precursor for the generation of extreme events in this system. These results are also true for electrical diffusive coupling. The distribution of the local maxima shows long tailed non-Gaussian while the interevent interval follows the Weibull distribution. The goodness of fit are corroborated using probability-probability plot and quantile-quantile plot. These extreme events become rarer and rarer with the increase in the number of different initial conditions.