Before revision: 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 J_0. When passing a lower threshold J^*_l  , 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.
After revision: 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 J_0. When passing a lower threshold J^*_l , a transition from desynchronization to 3-cluster burst synchronization occurs due to a constructive role of inhibition to favor population synchronization. In this case, the whole population is segregated into 3 clusters, and HR neurons in each cluster exhibit burst synchronization.