# American Institute of Mathematical Sciences

January  2022, 27(1): 229-243. doi: 10.3934/dcdsb.2021038

## The stability and bifurcation of homogeneous diffusive predator–prey systems with spatio–temporal delays

 School of Mathematics and Statistics, Henan Academy of Big Data, Zhengzhou University, Zhengzhou 450001, China

* Corresponding author: renjl@zzu.edu.cn

Received  August 2020 Revised  December 2020 Published  January 2022 Early access  January 2021

In this paper, we consider a generalized predator-prey system described by a reaction-diffusion system with spatio-temporal delays. We study the local stability for the constant equilibria of predator-prey system with the generalized delay kernels. Moreover, using the specific delay kernels, we perform a qualitative analysis of the solutions, including existence, uniqueness, and boundedness of the solutions; global stability, and Hopf bifurcation of the nontrivial equilibria.

Citation: Yiwen Tao, Jingli Ren. The stability and bifurcation of homogeneous diffusive predator–prey systems with spatio–temporal delays. Discrete & Continuous Dynamical Systems - B, 2022, 27 (1) : 229-243. doi: 10.3934/dcdsb.2021038
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##### References:
Some examples of $f(u)$ and $g(u)$. (a). Logistic effect (blue), weak Allee effect (red), strong Allee effect (green). (b). Type I function (blue), Type Ⅱ function (red), Type Ⅲ function (green)