Cluster Burst Synchronization in A Scale-Free Network of Inhibitory Bursting Neurons

Abstract

We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and investigate coupling-induced burst synchronization by varying the average coupling strength J0. When passing a lower threshold [Formula], a transition from desynchronization to 3-cluster burst synchronization occurs due to a constructive role of inhibition to favor the cluster burst synchronization. For this case, the whole population is segregated into 3 clusters, and HR neurons in each cluster exhibit burst synchronization. However, as J0 is increased and passes an intermediate threshold [Formula], HR neurons begin to make intermittent hoppings between the 3 clusters. Due to the intermittent intercluster hoppings, the 3 clusters are integrated into a single one. In spite of break-up of the 3 clusters, burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in J0, intercluster hoppings are intensified, and bursting stripes also become smeared more and more due to a destructive role of inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold [Formula] a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.\n\nPACS numbers: 87.19.lm, 87.19.lc