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. However, as J_0 is increased and passes an intermediate threshold J^*_m  , 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 J_0, 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 J^*_h  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.
We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and investigate coupling-induced cluster 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 ~(\simeq 0.78) , a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster exhibit burst synchronization. However, as J_0 passes an intermediate threshold J^*_m ~(\simeq 5.2) , 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, (non-cluster) 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 J_0, intercluster hoppings are intensified, and bursting stripes also become smeared more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold J^*_h ~(\simeq 17.8) 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.
A
cluster
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When passing a
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
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~(\simeq 0.78)
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from desynchronization
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a
another
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synaptic
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the cluster burst synchronization. For
population synchronization. In
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the whole population is segregated into 3 clusters, and
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is increased and
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~(\simeq 5.2)
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(non-cluster)
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synaptic
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~(\simeq 17.8)