Mathematical exploration on control of bifurcation for a 3D predator-prey model with delay

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

doi:10.3934/math.20241445

AIMS Mathematics

2024, Volume 9, Issue 11: 29883-29915. doi: 10.3934/math.20241445

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Research article

Mathematical exploration on control of bifurcation for a 3D predator-prey model with delay

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: 11 September 2024 Revised: 09 October 2024 Accepted: 11 October 2024 Published: 21 October 2024
MSC : 34C23, 34K18, 37GK15, 39A11, 92B20

In this current paper, we developed a new predator-prey model accompanying delay based on the earlier works. By applying inequality strategies, fixed point theorem, and a suitable function, we got new necessary conditions for the existence, uniqueness, nonnegativeness, and boundedness of the solution to the developed delayed predator-prey model. The bifurcation behavior and stability nature of the defined delayed predator-prey model were investigated by using stability and bifurcation theory of delayed differential equations. We have modified the Hopf bifurcation's appearance time and stability domain by building two distinct hybrid delayed feedback controllers for the delayed predator-prey model. The time of Hopf bifurcation appearance and stability domain of the model were explored. Matlab experiment diagrams were given to support the learned important results. The derived outcomes in this paper were original and have significant theoretical implications for maintaining equilibrium between the densities of the three species.
- predator-prey model,
- feature of solution,
- Hopf bifurcation,
- hybrid controller,
- delay,
- stability
Citation: Yingyan Zhao, Changjin Xu, Yiya Xu, Jinting Lin, Yicheng Pang, Zixin Liu, Jianwei Shen. Mathematical exploration on control of bifurcation for a 3D predator-prey model with delay[J]. AIMS Mathematics, 2024, 9(11): 29883-29915. doi: 10.3934/math.20241445

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Abstract

In this current paper, we developed a new predator-prey model accompanying delay based on the earlier works. By applying inequality strategies, fixed point theorem, and a suitable function, we got new necessary conditions for the existence, uniqueness, nonnegativeness, and boundedness of the solution to the developed delayed predator-prey model. The bifurcation behavior and stability nature of the defined delayed predator-prey model were investigated by using stability and bifurcation theory of delayed differential equations. We have modified the Hopf bifurcation's appearance time and stability domain by building two distinct hybrid delayed feedback controllers for the delayed predator-prey model. The time of Hopf bifurcation appearance and stability domain of the model were explored. Matlab experiment diagrams were given to support the learned important results. The derived outcomes in this paper were original and have significant theoretical implications for maintaining equilibrium between the densities of the three species.

References

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