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American Physical Society, Physical review E: Statistical, nonlinear, and soft matter physics, 3(83)

DOI: 10.1103/physreve.83.036209

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Traveling echo waves in an array of excitable elements with time-delayed coupling

Journal article published in 2011 by Oriol Vallès-Codina, Ronny Möbius, Sten Rüdiger, Lutz Schimansky-Geier
This paper is available in a repository.
This paper is available in a repository.

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Abstract

We study time-delayed coupling in one-dimensional arrays of discrete excitable FitzHugh-Nagumo elements. For small time delays in an excitatory coupling, noise-triggered spikes undergo a slight prolongation. For larger delay times, the coupling to adjacent elements leads to a splitting of spikes and an "echo" effect that produces dampened series of spikes. For very large delay times, a transition to a stationary regime appears, as the spikes are sustained by mutual excitations, resulting in antiphase synchronization of all elements. We characterize several features exhibited by the system, such as speed and duration of pulses as well as bifurcations leading to the stationary regime.