Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour

Zhenglong Chen, Shunjie Li () and Xuebing Zhang
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Zhenglong Chen: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Shunjie Li: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Xuebing Zhang: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Mathematics, 2022, vol. 10, issue 18, 1-20

Abstract: This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. Moreover, the Hopf bifurcation induced by the time delay variable is also investigated. Furthermore, the existence and non-existence of non-constant positive solutions are analyzed. Finally, numerical simulations are presented to validate the theoretical analysis.

Keywords: predator–prey system; fear effect; anti-predator behaviour; Hopf bifurcation; diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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