Invading activity fronts stabilize excitable systems against stochastic extinction

TL;DR

This paper demonstrates that invasion activity fronts can stabilize excitable systems against stochastic extinction by providing a continuous influx from stable regions, thus promoting species coexistence in spatially extended systems.

Contribution

It introduces the concept that invasion fronts can prevent stochastic extinction in excitable systems, with evidence from predator-prey, epidemic, and cyclic competition models.

Findings

Invasion fronts sustain activity in vulnerable regions, preventing extinction.

Diffusive coupling with stable patches enhances species persistence.

The mechanism applies across various ecological and epidemiological models.

Abstract

Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning control parameters may diminish the survival probability, rendering species coexistence susceptible to stochastic extinction events. In inhomogeneous settings, where a vulnerable subsystem is diffusively coupled to an adjacent stable patch, the former is reanimated through continuous influx from the interfaces, provided the absorbing region sustains spreading activity fronts. We demonstrate this generic elimination of finite-size extinction instabilities via immigration flux in predator-prey, epidemic spreading, and cyclic competition models.