Dynamics of a parabolic-ODE competition system in heterogeneous environments

Lou, Yuan; Salako, Rachidi

doi:10.1090/proc/14972

Dynamics of a parabolic-ODE competition system in heterogeneous environments
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by Yuan Lou and Rachidi B. Salako PDF

Proc. Amer. Math. Soc. 148 (2020), 3025-3038 Request permission

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 for 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.

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