Excitation waves on a minimal small-world model

Abstract

We examine traveling-wave solutions on a regular ring network with one additionallong-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics inthe excitable regime. The additional shortcut induces a plethora of spatio-temporalbehavior that is not present without it. We describe the underlying mechanisms fordifferent types of patterns: propagation failure, period decreasing, bistability, shortcutblocking and period multiplication. For this purpose, we investigate the dependence ond, thenetwork size, the coupling range in the original ring and the global coupling strength andpresent a phase diagram summarizing the different scenarios. Furthermore, we discuss thescaling behavior of the critical distance by analytical means and address the connectionto spatially continuous excitable media.