Dynamic analysis and optimal control of a fractional order predator-prey model with economic threshold

Wenjun Gao; Xiaoyan Tian; Ruiqing Shi; Wenjun Gao; Xiaoyan Tian; Ruiqing Shi

doi:10.3934/era.2025205

Electronic Research Archive

2025, Volume 33, Issue 8: 4529-4558. doi: 10.3934/era.2025205

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Research article

Dynamic analysis and optimal control of a fractional order predator-prey model with economic threshold

1.
School of Economics and Management, Shanxi Normal University, Taiyuan 030031, China
2.
School of Mathematics Science, Shanxi Normal University, Taiyuan 030031, China

Received: 04 June 2025 Revised: 15 July 2025 Accepted: 31 July 2025 Published: 06 August 2025

In this paper, a fractional order differential algebraic predator-prey system with Holling type functional response was presented. The dynamic behavior of populations under the influence of economic benefits was thoroughly investigated. Specifically, with economic benefit as the bifurcation parameter, the existence of singularity-induced bifurcation was analyzed based on the theory of differential algebraic system. After that, a state feedback controller was designed to eliminate the singularity induced bifurcation and stabilize the system near the corresponding interior equilibrium. Furthermore, an optimal control problem was formulated, and the necessary conditions were derived. In addition, the validity of the theoretical results was confirmed through extensive numerical simulations.
- predator-prey model,
- fractional order,
- differential algebraic equations,
- singularity-induced bifurcation,
- stability,
- optimal control
Citation: Wenjun Gao, Xiaoyan Tian, Ruiqing Shi. Dynamic analysis and optimal control of a fractional order predator-prey model with economic threshold[J]. Electronic Research Archive, 2025, 33(8): 4529-4558. doi: 10.3934/era.2025205

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Abstract

In this paper, a fractional order differential algebraic predator-prey system with Holling type functional response was presented. The dynamic behavior of populations under the influence of economic benefits was thoroughly investigated. Specifically, with economic benefit as the bifurcation parameter, the existence of singularity-induced bifurcation was analyzed based on the theory of differential algebraic system. After that, a state feedback controller was designed to eliminate the singularity induced bifurcation and stabilize the system near the corresponding interior equilibrium. Furthermore, an optimal control problem was formulated, and the necessary conditions were derived. In addition, the validity of the theoretical results was confirmed through extensive numerical simulations.

References

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