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.
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. For sufficiently small J_0, non-cluster desynchronized states exist. However, when passing a critical point J^*_c~(\simeq 0.16), the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As J_0 is further increased and passes 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.