# Front interaction induces excitable behavior

## TL;DR

This paper introduces a novel mechanism for excitability in spatially extended systems, where front interactions between two stable states induce long-lived transient structures without oscillatory dynamics.

## Contribution

It presents a new excitability mechanism based on front interactions and coexistence of stable states, expanding understanding beyond local excitability and localized structures.

## Key findings

- Existence of a threshold for perturbations leading to long-lived structures
- Super-threshold perturbations cause fronts to approach and annihilate
- Extended systems without oscillations can exhibit excitability

## Abstract

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.