Excitation Waves on a Minimal Small-World Model

Abstract

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

14 pages, 11 figures

References in corpus (8)

• Turing patterns in network-organized activator-inhibitor systems
• Emergence of self-sustained patterns in small-world excitable media
• Traveling and pinned fronts in bistable reaction-diffusion systems on network
• Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback
• Propagation failure of excitation waves on trees and random networks
• Nonlocal control of pulse propagation in excitable media
• Effect of small-world topology on wave propagation on networks of excitable elements
• Front and Turing patterns induced by Mexican-hat-like nonlocal feedback