Spike synchronization in a small-world network

In this paper we examine the effects of small-world network organization on spike synchronization dynamics in networks of Izhikevich spiking units. We interpolate network organizations from regular ring lattices, through the small-world region, to random networks, and measure global spike synchronization dynamics. We examine how average path length and clustering effect the dynamics of global and neighborhood clique spike organization and propagation. We show that the emergence of global synchronization undergoes a phase transition in the small-world region, between the clustering and path length phase transitions that are known to exist. We add additional realistic constraints on the dynamics by introducing propagation delays of spiking signals proportional to wiring length. The addition of delays interferes with the ability of random networks to sustain global synchronization, in relation to the breakdown of clustering in the networks. The addition of delays further enhances the finding that small-world organization is beneficial for balancing neighborhood synchronized waves of organization with global synchronization dynamics.