Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting

Huangyu Guo, Jing Han and Guodong Zhang ()
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Huangyu Guo: School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
Jing Han: School of Information Engineering, Wuhan Business University, Wuhan 430056, China
Guodong Zhang: School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China

Mathematics, 2023, vol. 11, issue 24, 1-18

Abstract: In this essay, we introduce a bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting. Due to the introduction of nonlinear prey harvesting, the model demonstrates intricate dynamic behaviors in the predator–prey plane. Economic profit serves as a bifurcation parameter for the system. The stability and Hopf bifurcation of the model are discussed through normal forms and bifurcation theory. These results reveal richer dynamic features of the bioeconomic predator–prey model which incorporates the square root functional response and nonlinear prey harvesting, and provides guidance for realistic harvesting. A feedback controller is introduced in this paper to move the system from instability to stability. Moreover, we discuss the biological implications and interpretations of the findings. Finally, the results are validated by numerical simulations.

Keywords: bioeconomic systems; predator–prey models; non-linear prey harvesting; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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