Bifurcation and controller design in a 3D delayed predator-prey model

Jinting Lin; Changjin Xu; Yiya Xu; Yingyan Zhao; Yicheng Pang; Zixin Liu; Jianwei Shen; Jinting Lin; Changjin Xu; Yiya Xu; Yingyan Zhao; Yicheng Pang; Zixin Liu; Jianwei Shen

doi:10.3934/math.20241617

AIMS Mathematics

2024, Volume 9, Issue 12: 33891-33929. doi: 10.3934/math.20241617

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Research article

Bifurcation and controller design in a 3D delayed predator-prey model

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
2.
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, China
3.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
4.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China

Received: 20 September 2024 Revised: 07 November 2024 Accepted: 14 November 2024 Published: 29 November 2024
MSC : 34C23, 34K18, 37GK15, 39A11, 92B20

Delayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this article construct a novel delayed predator-prey model. By utilizing fixed point theory, inequality methods, and appropriate functions, this article examined the desirable properties of the solutions of the constructed delayed predator-prey system, including existence and uniqueness, boundedness, and non-negativity. This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. The research explores how delays affect the stabilization of system and the adjustment of bifurcation. This paper provides computer simulation photos supporting the main obtained findings. The outcomes of this paper are groundbreaking and can provide critical guidance for the control and regulation of predator and prey population densities.
- predator-prey system,
- well-posedness of solution,
- Hopf bifurcation,
- stability,
- hybrid controller
Citation: Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen. Bifurcation and controller design in a 3D delayed predator-prey model[J]. AIMS Mathematics, 2024, 9(12): 33891-33929. doi: 10.3934/math.20241617

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Abstract

Delayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this article construct a novel delayed predator-prey model. By utilizing fixed point theory, inequality methods, and appropriate functions, this article examined the desirable properties of the solutions of the constructed delayed predator-prey system, including existence and uniqueness, boundedness, and non-negativity. This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. The research explores how delays affect the stabilization of system and the adjustment of bifurcation. This paper provides computer simulation photos supporting the main obtained findings. The outcomes of this paper are groundbreaking and can provide critical guidance for the control and regulation of predator and prey population densities.

References

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