Research ArticleFree Access

Bifurcation analysis of a diffusive predator–prey model with hyperbolic mortality and prey-taxis

Yan Li

College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China

E-mail Address: liyan@upc.edu.cn

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Zhiyi Lv

College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China

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Fengrong Zhang

College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China

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, and

Hui Hao

College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China

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https://doi.org/10.1142/S1793524523500110Cited by:1 (Source: Crossref)

Abstract

In this paper, we study a diffusive predator–prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition. We first analyze the influence of prey-taxis on the local stability of constant equilibria. It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium, but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium. We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis, which imply that the prey-taxis plays an important role in the dynamics.

Keywords:

AMSC: 35E15, 35J57, 92B05, 35Q92

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