Bifurcation analysis of a reaction-diffusion-advection predator-prey system with delay

Honghua Bin; Daifeng Duan; Junjie Wei; Honghua Bin; Daifeng Duan; Junjie Wei

doi:10.3934/mbe.2023543

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12194-12210. doi: 10.3934/mbe.2023543

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Bifurcation analysis of a reaction-diffusion-advection predator-prey system with delay

1.
Department of Mathematics, Jimei University, Jimei, Fujian 361021, China
2.
Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China

Academic Editor: Xiang-Sheng Wang

Received: 17 April 2023 Revised: 11 May 2023 Accepted: 12 May 2023 Published: 17 May 2023

A diffusive predator-prey system with advection and time delay is considered. Choosing the conversion delay $ \tau $ as a bifurcation parameter, we find that as $ \tau $ varies, the system will generate Hopf bifurcation. Then, for the reaction diffusion model proposed in this paper, we use an improved center manifold reduction method and normal form theory to derive an algorithm for determining the direction and stability of Hopf bifurcation. Finally, we provide simulations to illustrate the effects of time delay $ \tau $ and advection $ \alpha $ on system behaviors.
- conversion delay,
- diffusion,
- advection,
- Hopf bifurcation
Citation: Honghua Bin, Daifeng Duan, Junjie Wei. Bifurcation analysis of a reaction-diffusion-advection predator-prey system with delay[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12194-12210. doi: 10.3934/mbe.2023543

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Abstract

A diffusive predator-prey system with advection and time delay is considered. Choosing the conversion delay $ \tau $ as a bifurcation parameter, we find that as $ \tau $ varies, the system will generate Hopf bifurcation. Then, for the reaction diffusion model proposed in this paper, we use an improved center manifold reduction method and normal form theory to derive an algorithm for determining the direction and stability of Hopf bifurcation. Finally, we provide simulations to illustrate the effects of time delay $ \tau $ and advection $ \alpha $ on system behaviors.

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