Noise-Induced Burst and Spike Synchronizations in An Inhibitory Small-World Network of Subthreshold Bursting Neurons

摘要

For modeling complex synaptic connectivity, we consider the Watts-Strogatzsmall-world network which interpolates between regular lattice and randomnetwork via rewiring, and investigate the effect of small-world connectivity onemergence of noise-induced population synchronization in an inhibitorypopulation of subthreshold bursting Hindmarsh-Rose neurons. Thus, noise-inducedslow burst synchronization and fasg spike synchronization are found to appearin a synchronized region of the $J-D$ plane. As the rewiring probability $p$ isdecreased from 1 (random network) to 0 (regular lattice), the region of spikesynchronization shrinks rapidly in the $J-D$ plane, while the region of theburst synchronization decreases slowly. Population synchronization may be wellvisualized in the raster plot of neural spikes which can be obtained inexperiments. Instantaneous population firing rate, $R(t)$, which is directlyobtained from the raster plot of spikes, is a realistic population quantityexhibiting collective behaviors with both the slow bursting and the fastspiking timescales. Through frequency filtering, we separate $R(t)$ into$R_b(t)$ (describing the slow bursting behavior) and $R_s(t)$ (describing thefast intraburst spiking behavior). Then, we develop thermodynamic orderparameters and statistical-mechanical measures, based on $R_b (t)$ and $R_s(t)$, for characterization of the burst and spike synchronizations of thebursting neurons and show their usefulness in explicit examples. With increasein $p$, both the degrees of the burst and spike synchronizations are found toincrease because more long-range connections appear. However, they becomesaturated for some maximal values of $p$ because long-range short-cuts whichappear up to the maximal values of $p$ play sufficient role to get maximaldegrees of the burst and spike synchronizations.