Unbounded autocatalytic growth on diffusive substrate: the extinction transition

TL;DR

This paper investigates how spatial fluctuations influence the survival or extinction of autocatalytic agents, revealing that adaptation can promote proliferation even when mean field models predict extinction, with extinction times following a power law.

Contribution

It demonstrates numerically that spatial fluctuations and adaptation enable proliferation beyond mean field predictions, highlighting the role of spatial correlations in extinction transitions.

Findings

Proliferation occurs despite mean field extinction predictions due to spatial fluctuations.

Extinction times follow a power-law distribution in the studied parameter region.

The system exhibits a characteristic exponential growth phase in the proliferation regime.

Abstract

The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to proliferation even if the mean field rate equations predict extinction, in agreement with previous theoretical predictions. While in the proliferation phase the system admits a typical time scale that dictates the exponential growth, the extinction times distribution obeys a power law at the parameter region considered.