Dynamics of a diffusive predator-prey system with fear effect in advective environments

We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary conditions, as well as Free-Flow (FF) boundary conditions. Our investi...

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Bibliographic Details
Main Authors Duan, Daifeng, Niu, Ben, Yuan, Yuan
Format Journal Article
LanguageEnglish
Published 01.12.2023
Subjects
Mathematics - Dynamical Systems
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Summary:We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary conditions, as well as Free-Flow (FF) boundary conditions. Our investigation focuses on determining the direction and stability of spatial Hopf bifurcation, with the generation delay $\tau$ serving as the bifurcation parameter. Additionally, we examine the influence of both linear and Holling-II functional responses on the dynamics of the model. Through these analyses, we aim to gain a better understanding of the intricate relationship between advection, predation, and prey response in this system.
DOI:10.48550/arxiv.2312.00395