Multiple bifurcations in a predator–prey system of modified Holling and Leslie type with double Allee effect and nonlinear harvesting

Zuchong Shang and Yuanhua Qiao

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 745-764

Abstract: In this paper, a modified Leslie-type predator–prey model with simplified Holling type IV functional response is established, in which double Allee effect on prey and nonlinear prey harvesting are considered. The analysis of the model shows that there exists a Bogdanov–Takens singularity (focus case) of codimension 4, and also multiple other nonhyperbolic and degenerate equilibria. Bifurcations are explored and it is found that transcritical bifurcation, saddle–node bifurcation, Bogdanov–Takens bifurcation of codimension 2, degenerate cusp type Bogdanov–Takens bifurcation of codimension 3, and degenerate focus type Bogdanov–Takens bifurcation of codimension 4 occur as parameters vary. The bifurcations result in complex dynamic behaviors, such as double limit cycle, triple limit cycle, quadruple limit cycle, cuspidal loop, (multiple) homoclinic loop, saddle–node loop, and limit cycle(s) simultaneously with homoclinic loop. We run numerical simulations to verify the theoretical results, and it is found that the system admits bistability, tristability, or even tetrastability.

Keywords: Predator–prey model; Double Allee effect; Nonlinear harvesting; Degenerate focus type Bogdanov–Takens bifurcation of codimension 4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:745-764

DOI: 10.1016/j.matcom.2022.10.028

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