Global dynamics of a Lotka-Volterra competition system in an advective patchy environment

Qi Wang

doi:10.3934/dcdsb.2024103

Article Contents

2025, Volume 30, Issue 2: 604-628. Doi: 10.3934/dcdsb.2024103

This issue Previous Article Carleman linearization of nonlinear systems and its finite-section approximations Next Article Well-posedness and dynamics of wave equations with nonlinear damping and moving boundary

Global dynamics of a Lotka-Volterra competition system in an advective patchy environment

Qi Wang

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received: April 2024

Revised: July 2024

Early access: August 12, 2024

Published online: August 12, 2024

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Abstract

In this paper, we consider a two-species competition-advection patchy model, where individuals cannot pass through the upstream patch and do not return to the habitat after leaving the downstream patch. We study the dynamics of steady states. By applying the theory of principal eigenvalue, we first obtain two critical curves ($ \Gamma_1 $ and $ \Gamma_2 $) in the plane of $ q_1-q_2 $ that sharply determine the local stability of the two semitrivial steady states. Afterwards, we verify the global dynamics under various conditions on given parameters by some analytic approaches.

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Mathematics Subject Classification: Primary: 34C12, 34D20, 34D23, 37C65, 37C75; Secondary: 92D25, 92D40.

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Figure 1. A stream with $ n $ patches, where $ d $ is the random movement rate and $ q $ is the directed drift rate. Patch $ 1 $ is the upstream end, and patch $ n $ is the downstream end

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Figure 2. The curves of $ u_1,u_2,u_3 $

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