Stability and Hopf Bifurcation in a Predator-Prey Model with the Cost of Anti-Predator Behaviors

被引：31
|
作者：
Qiao, Ting [1 ,2 ]
Cai, Yongli [1 ]
Fu, Shengmao [2 ]
Wang, Weiming [1 ]
机构：
[1] Huaiyin Normal Univ, Sch Math & Stat, Huaian 223300, Peoples R China
[2] Northwest Normal Univ, Sch Math & Stat, Lanzhou 730070, Gansu, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2019年 / 29卷 / 13期
基金：
美国国家科学基金会;
关键词：
Beddington-DeAngelis functional response; fear factor; stability; Hopf bifurcation; EPIDEMIC MODEL; TRANSMISSION DYNAMICS; RISK; PATTERNS;
D O I：
10.1142/S0218127419501852
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate the influence of anti-predator behavior in prey due to the fear of predators with a Beddington-DeAngelis prey-predator model analytically and numerically. We give the existence and stability of equilibria of the model, and provide the existence of Hopf bifurcation. In addition, we investigate the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also prevent the occurrence of limit cycle oscillation and increase the stability of the system.
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收藏
页数：10
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