Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

doi:10.3969/j.issn.1006-8074.2024.03.005

Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (3): 67-.doi: 10.3969/j.issn.1006-8074.2024.03.005

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Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

Shen Zhongyuan^1,2, Zhang Xuebing^1,2,*, Li Shunjie^1,2

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China; 2. Center for Applied Mathematics of Jiangsu Province, Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing 210044, China

Online:2024-09-28 Published:2024-11-06
Contact: Zhang Xuebing (1980–), Associate Professor, PhD; E-mail: zxb1030@163.com
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 12271261) and the National Undergraduate Training Program for Innovation and Entrepreneurship (No. 202310300044Z)

Abstract

Abstract: In this paper, we establish a delayed predator-prey model with nonlocal fear effect. Firstly, the existence, uniqueness, and persistence of solutions of the model are studied. Then, the local stability, Turing bifurcation, and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic equation. The global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function method. Finally, the correctness of the theoretical analysis results is verified through numerical simulations.

Key words: Delay , Nonlocal fear effect, Global stability, Hopf bifurcation

Shen Zhongyuan, Zhang Xuebing, Li Shunjie. Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect[J]. Mathematical Theory and Applications, 2024, 44(3): 67-.

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Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

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