  We study excitation waves on a Newman-Watts small-world network model of
coupled excitable elements. Depending on the global coupling strength, we find
differing resilience to the added long-range links and different mechanisms of
propagation failure. For high coupling strengths, we show agreement between the
network and a reaction-diffusion model with additional mean-field term.
Employing this approximation, we are able to estimate the critical density of
long-range links for propagation failure.
