Diversity-induced synchronized oscillations in close-to-threshold excitable elements arranged on regular networks: Effects of network topology

The question of how network topology influences emergent synchronized oscillations in excitable media is addressed. Coupled van der Pol–FitzHugh–Nagumo elements arranged either in regular rings or in the square lattice networks are investigated. Clustered and declustered rings are constructed to have the same node connectivity (the same number of links). The systems are chosen to be close-to-threshold, allowing global oscillations to be triggered by a weak diversity among the constituents that, by themselves, would be non-oscillating. The results clearly illustrate the crucial role played by network topology. In particular we found that network performance (activity and synchronization) is mainly determined by the network average path length. The shorter the average path length, the better the network performance. Local properties, as characterized by the clustering coefficient, are less important. In addition we consider the dependence of global oscillations on the size of the system and comment on the mechanisms that sustain synchronized oscillations.