Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions

Xiangjun Dai, Hui Jiao, Jianjun Jiao () and Qi Quan
Additional contact information
Xiangjun Dai: School of Date Science, Tongren University, Tongren 554300, China
Hui Jiao: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
Jianjun Jiao: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Qi Quan: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Mathematics, 2023, vol. 11, issue 18, 1-19

Abstract: In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a fear effect, in the presence of predators. Applying the Floquet theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the stability of the prey-extinction periodic solution and the permanence of the system. Furthermore, we also study the case where the prey population does not migrate. Sufficient conditions for the stability of the prey-extinction periodic solution and the permanence are also established, and the threshold for extinction and permanence of the prey population is obtained. Finally, some numerical simulations are provided to verify the theoretical results. These results provide a theoretical foundation for the conservation of biodiversity.

Keywords: predator–prey system; fear effect; refuge effect; persistence; global stability (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/2227-7390/11/18/3838/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/18/3838/ (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:18:p:3838-:d:1235105

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 ().