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

¹ Departamento de Fisica Aplicada, Instituto Universitario de Materiales and Unidad Asociada del Consejo Superior de Investigaciones Científicas Universidad de Alicante - E-03080 Alicante, Spain
² Departament de Física Fonamental, Universitat de Barcelona E-08028 Barcelona, Spain

Received: 15 June 2006
Accepted: 2 October 2006

Abstract

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.