Front interaction induces excitable behavior

Parra-Rivas, P.; Matias, M.A.; Colet, P.; Gelens, L.; Walgraef, D.; Gomila, D.
Physical Review E 95, 020201(R) (1-4) (2017)

Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an alternative mechanism based on the coexistence of two homogeneous stable states and spatial coupling. We show the existence of a threshold for perturbations of the homogeneous state. Sub-threshold perturbations decay exponentially. Super-threshold perturbations induce the emergence of a long-lived structure formed by two back to back fronts that join the two homogeneous states. While in typical excitability the trajectory follows the remnants of a limit cycle, here reinjection is provided by front interaction, such that fronts slowly approach each other until eventually annihilating. This front-mediated mechanism shows that extended systems with no oscillatory regimes can display excitability.

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