Stability Analysis and Hopf Bifurcation of a Delayed Diffusive Predator–Prey Model with a Strong Allee Effect on the Prey and the Effect of Fear on the Predator

Yining Xie, Jing Zhao and Ruizhi Yang ()
Additional contact information
Yining Xie: School of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
Jing Zhao: School of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
Ruizhi Yang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2023, vol. 11, issue 9, 1-15

Abstract: In this paper, we propose a diffusive predator–prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. We mainly study the local stability of the coexisting equilibrium and the existence and properties of Hopf bifurcation. We provide bifurcation diagrams with the fear effect parameter ( s ) and the Allee effect parameter ( a ), showing that the stable region of the coexisting equilibrium increases (or decreases) with an increase in the fear effect parameter ( s ) (or the Allee effect parameter ( a )). We also show that gestation delay ( τ ) can affect the local stability of the coexisting equilibrium. When the delay ( τ ) is greater than the critical value, the coexistence equilibrium loses its stability, and bifurcating periodic solutions appear. Whether the bifurcated periodic solution is spatially homogeneous or inhomogeneous depends on the fear effect parameter ( s ) and the Allee effect parameter ( a ). These results show that the fear effect parameter ( s ), the Allee effect parameter ( a ), and gestation delay ( τ ) can be used to control the growth of prey and predator populations.

Keywords: delay; Hopf bifurcation; predator–prey; Allee effect (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/1996/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/1996/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:1996-:d:1130854

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().