Abstract
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.
Highlights
Excitable media are well studied model systems in a variety of applications ranging from chemical [1] to electronic systems [2] and lasers [3] and from heart-muscle tissue [4] to neural systems [5, 6]
As a generic model of excitable dynamics we use the FitzHugh-Nagumo model [36, 37] on an undirected, unweighted network, where neighboring nodes are coupled by the difference in the activator concentrations
We find the same behavior as expected by the dispersion relation of Eq (6)
Summary
Excitable media are well studied model systems in a variety of applications ranging from chemical [1] to electronic systems [2] and lasers [3] and from heart-muscle tissue [4] to neural systems [5, 6]. In recent years dynamical systems coupled in complex network architectures have attracted a lot of attention [16, 17, 18, 19, 20] Those systems can occur in a wide variety of applications ranging from power grids [21] to biological networks [22]. Scenarios with excitable elements coupled in a chain-like one-dimensional topology have been suggested as a mechanism for the occurrence of traveling waves of activity in the visual cortex [11]. We attempt to do so by using a generic model of excitability, the well-known FitzHugh-Nagumo model [36, 37], combined with a Newman-Watts small-world architecture [17] as well as techniques from spatially continuous systems to study the behavior of excitation waves.
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