Invading activity fronts or near-critical clusters may stabilize vulnerable excitable systems against stochastic trajectories terminating in an absorbing state

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 the absorbing configuration (e.g., species extinction or fixation) becomes exceedingly long. Tuning control parameters may effectively diminish the survival probability, rendering active states (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 re-activated through influx from the interfaces, provided the vulnerable region either sustains spreading activity fronts or near-critical large active clusters. Either dynamical structure resets the system to correlated initial conditions favorable for survival. We demonstrate this generic elimination of finite-size extinction instabilities via immigration flux in stochastic predator-prey, cyclic competition, and epidemic spreading models.

arXiv comment6 pages, 3 figures, supplementary material included as ancillary pdf file