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Fast cortical rhythms with stochastic and intermittent neural discharges havebeen observed in electric recordings of brain activity. Recently, Brunel et al.developed a framework to describe this kind of fast sparse synchronization inboth random and globally-coupled networks of suprathreshold spiking neurons.However, in a real cortical circuit, synaptic connections are known to havecomplex topology which is neither regular nor random. Hence, in order to extendthe works of Brunel et al. to realistic neural networks, we study the effect ofnetwork architecture on these fast sparsely synchronized rhythms in aninhibitory population of suprathreshold fast spiking (FS) Izhikevichinterneurons. We first employ the conventional Erd\"{o}s-Renyi random graph ofsuprathreshold FS Izhikevich interneurons for modeling the complex connectivityin neural systems, and study emergence of the population synchronized states byvarying both the synaptic inhibition strength $J$ and the noise intensity $D$.Thus, fast sparsely synchronized states of relatively high degree are found toappear for large values of $J$ and $D$. Second, for fixed values of $J$ and $D$where fast sparse synchronization occurs in the random network, we consider theWatts-Strogatz small-world network of suprathreshold FS Izhikevich interneuronswhich interpolates between regular lattice and random graph via rewiring, andinvestigate the effect of small-world synaptic connectivity on emergence offast sparsely synchronized rhythms by varying the rewiring probability $p$ fromshort-range to long-range connection. When passing a small critical value$p^*_c$ $(\simeq 0.12)$, fast sparsely synchronized population rhythms arefound to emerge in small-world networks with predominantly local connectionsand rare long-range connections.

Effect of Small-World Connectivity on Fast Sparsely Synchronized Cortical Rhythms