Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay

Yurong Dong, Hua Liu (), Yumei Wei, Qibin Zhang and Gang Ma
Additional contact information
Yurong Dong: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
Hua Liu: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
Yumei Wei: Experimental Teaching Department, Northwest Minzu University, Lanzhou 730030, China
Qibin Zhang: Gansu High-Tech Innovation Service Center, Lanzhou 730030, China
Gang Ma: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China

Mathematics, 2024, vol. 12, issue 18, 1-24

Abstract: The purpose of this paper is to study a predator–prey model with Allee effect and double time delays. This research examines the dynamics of the model, with a focus on positivity, existence, stability and Hopf bifurcations. The stability of the periodic solution and the direction of the Hopf bifurcation are elucidated by applying the normal form theory and the center manifold theorem. To validate the correctness of the theoretical analysis, numerical simulations were conducted. The results suggest that a weak Allee effect delay can promote stability within the model, transitioning it from instability to stability. Nevertheless, the competition delay induces periodic oscillations and chaotic dynamics, ultimately resulting in the population’s collapse.

Keywords: Allee effect; Hopf bifurcation; delay; center manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/18/2853/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/18/2853/ (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:12:y:2024:i:18:p:2853-:d:1477899

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 ().