Stability and Turing Patterns of a Predator-prey Model with Holling Type Ⅱ Functional Response and Allee Effect in Predator  

作　　者：Lu CHEN Feng YANG Yong-li SONG 

机构地区：[1]School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第3期675-695,共21页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China (No.11971143;12071105);Zhejiang Provincial Natural Science Foundation of China (No.LZ23A010001)。

摘　　要：In this paper, we are concerned with a predator-prey model with Holling type Ⅱ functional response and Allee effect in predator. We first mathematically explore how the Allee effect affects the existence and stability of the positive equilibrium for the system without diffusion. The explicit dependent condition of the existence of the positive equilibrium on the strength of Allee effect is determined. It has been shown that there exist two positive equilibria for some modulate strength of Allee effect. The influence of the strength of the Allee effect on the stability of the coexistence equilibrium corresponding to high predator biomass is completely investigated and the analytically critical values of Hopf bifurcations are theoretically determined.We have shown that there exists stability switches induced by Allee effect. Finally, the diffusion-driven Turing instability, which can not occur for the original system without Allee effect in predator, is explored, and it has been shown that there exists diffusion-driven Turing instability for the case when predator spread slower than prey because of the existence of Allee effect in predator.

关 键 词：predator-prey model Allee effect DIFFUSION STABILITY Turing bifurcation 

分 类 号：O175[理学—数学] Q141[理学—基础数学]