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

Ting Qiao

School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, P. R. China

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. China

E-mail Address: tingqiao33@163.com

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Yongli Cai

School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, P. R. China

E-mail Address: caiyongli@hytc.edu.cn

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Shengmao Fu

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. China

E-mail Address: fusm@nwnu.edu.cn

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, and

Weiming wang

http://orcid.org/0000-0002-7562-8260

School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, P. R. China

E-mail Address: wangwm_math@hytc.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218127419501852Cited by:29 (Source: Crossref)

Abstract

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.

Keywords:

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