Performance of excitable small-world networks of Bonhoeffer-van der Pol-FitzHugh-Nagumo oscillators

We investigate how performance (i.e. activity of the nodes and their subsequent synchronization) of excitable small-world networks depends on network topology. Network elements are described by Bonhoeffer-van der Pol-FitzHugh-Nagumo oscillators assumed to be close to the oscillating threshold. Global oscillations are induced by introducing a small amount of diversity. In homogeneous networks, it is found that the system performance is mainly determined by the average path length, no matter what the local properties are. The network undergoes a transition from low to high activity regimes at a critical path length. This transition, also found in regular networks, is shown to be caused by the dependence of the critical coupling strength between network units on the average path length.