An analysis of a predator-prey model in which fear reduces prey birth and death rates

Yalong Xue; Fengde Chen; Xiangdong Xie; Shengjiang Chen; Yalong Xue; Fengde Chen; Xiangdong Xie; Shengjiang Chen

doi:10.3934/math.2024630

AIMS Mathematics

2024, Volume 9, Issue 5: 12906-12927. doi: 10.3934/math.2024630

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Research article

An analysis of a predator-prey model in which fear reduces prey birth and death rates

1.
College of Mathematics and Physics, Ningde Normal University, Ningde 352100, Fujian, China
2.
School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, Fujian, China

Received: 02 January 2024 Revised: 13 March 2024 Accepted: 25 March 2024 Published: 07 April 2024
MSC : 34C23, 34D23

We have combined cooperative hunting, inspired by recent experimental studies on birds and vertebrates, to develop a predator-prey model in which the fear effect simultaneously influences the birth and mortality rates of the prey. This differs significantly from the fear effect described by most scholars. We have made a comprehensive analysis of the dynamics of the model and obtained some new conclusions. The results indicate that both fear and cooperative hunting can be a stable or unstable force in the system. The fear can increase the density of the prey, which is different from the results of all previous scholars, and is a new discovery in our study of the fear effect. Another new finding is that fear has an opposite effect on the densities of two species, which is different from the results of most other scholars in that fear synchronously reduces the densities of both species. Numerical simulations have also revealed that the fear effect extends the time required for the population to reach its survival state and accelerates the process of population extinction.
- prey-predator,
- fear effect,
- cooperative hunting,
- bifurcation
Citation: Yalong Xue, Fengde Chen, Xiangdong Xie, Shengjiang Chen. An analysis of a predator-prey model in which fear reduces prey birth and death rates[J]. AIMS Mathematics, 2024, 9(5): 12906-12927. doi: 10.3934/math.2024630

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Abstract

We have combined cooperative hunting, inspired by recent experimental studies on birds and vertebrates, to develop a predator-prey model in which the fear effect simultaneously influences the birth and mortality rates of the prey. This differs significantly from the fear effect described by most scholars. We have made a comprehensive analysis of the dynamics of the model and obtained some new conclusions. The results indicate that both fear and cooperative hunting can be a stable or unstable force in the system. The fear can increase the density of the prey, which is different from the results of all previous scholars, and is a new discovery in our study of the fear effect. Another new finding is that fear has an opposite effect on the densities of two species, which is different from the results of most other scholars in that fear synchronously reduces the densities of both species. Numerical simulations have also revealed that the fear effect extends the time required for the population to reach its survival state and accelerates the process of population extinction.

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