Dynamical properties of spiking neural networks with small world topologies.

Abstract Spiking neural networks can exhibit complex firing regimes whose characteristics are influenced by network topology. This paper is part of an investigation into the dynamical properties of spiking neural networks generated with small world topologies in comparison to those generated with Erdos-Renyi random graphs. Specifically, the parameters for small world and random graph network topology generation are tested empirically to find values which give rise to stable (fixed or periodic) vs. unstable or dissipative firing patterns. Similar to Erdos-Renyi random graph topologies, a critical threshold was found where the parameters of small world network generation lead to stable rather than dissipative patterns. Optimal parameters are identified for both small world and Erdos-Renyi random graph topologies which allow for stable firing patterns with minimal synapses. These results suggest questions that will form the basis for further research into the effects of topology class on firing dynamics of spiking neural networks.