Stability and instability of constant stationary solutions to some integro-differential equations

TL;DR

This paper investigates the stability of constant stationary solutions in reaction-diffusion integro-differential equations with nonlocal resource consumption and competition, providing precise coefficient conditions for stability and instability.

Contribution

It offers new sharp criteria for stability and instability of stationary solutions in nonlocal reaction-diffusion models, advancing understanding of their dynamic behavior.

Findings

Derived explicit stability conditions for stationary solutions

Identified parameter regimes leading to instability

Enhanced theoretical understanding of nonlocal reaction-diffusion systems

Abstract

We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of nontrivial constant stationary solutions.