Dynamics of a parabolic-ODE competition system in heterogeneous environments

TL;DR

This paper analyzes the long-term behavior of a hybrid parabolic-ODE system modeling two competing populations with different movement strategies, revealing conditions for extinction and coexistence in heterogeneous environments.

Contribution

It provides new insights into how movement behaviors influence competition outcomes in heterogeneous environments, especially the impact of sinks on population persistence.

Findings

Non-diffusing population drives diffusing one to extinction in sink environments.

Coexistence is possible in environments without sinks.

Movement behavior critically affects long-term population dynamics.

Abstract

This work is concerned with the large time behavior of the solutions of a parabolic-ODE hybrid system, modeling the competition of two populations which are identical except their movement behaviors: one species moves by random dispersal while the other does not diffuse. We show that the non-diffusing population will always drive the diffusing one to extinction in environments with sinks. In contract, the non-diffusing and diffusing populations can coexist in environments without sinks.