A diffusive predator-prey system with advection and time delay is considered. Choosing the conversion delay τ as a bifurcation parameter, we find that as τ 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 τ and advection α on system behaviors.
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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A diffusive predator-prey system with advection and time delay is considered. Choosing the conversion delay τ as a bifurcation parameter, we find that as τ 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 τ and advection α on system behaviors.
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