A phase diagram for a stochastic reaction diffusion system

TL;DR

This paper develops a phase diagram for a stochastic reaction-diffusion model that predicts whether a population will survive or go extinct based on key parameters, accounting for individual noise effects.

Contribution

It introduces a two-parameter phase diagram for a stochastic reaction-diffusion system modeling population-resource interactions with noise.

Findings

Phase diagram distinguishes survival and extinction regions.

Large time behavior depends on model parameters.

Inclusion of individual noise impacts population dynamics.

Abstract

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is established to describe the large time evolution, distinguishing between certain death or possible life of the population.