Bifurcation analysis of a food chain chemostat model with Michaelis-Menten functional response and double delays

Xin Xu; Yanhong Qiu; Xingzhi Chen; Hailan Zhang; Zhiyuan Liang; Baodan Tian; Xin Xu; Yanhong Qiu; Xingzhi Chen; Hailan Zhang; Zhiyuan Liang; Baodan Tian

doi:10.3934/math.2022676

AIMS Mathematics

2022, Volume 7, Issue 7: 12154-12176. doi: 10.3934/math.2022676

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Bifurcation analysis of a food chain chemostat model with Michaelis-Menten functional response and double delays

1.
College of Mathematics and Physics, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
2.
College of Mathematics and Statistics, Chongqing University, Chongqing 400000, China

Received: 11 February 2022 Revised: 04 April 2022 Accepted: 13 April 2022 Published: 22 April 2022
MSC : 34D05, 37N25, 92B05

In this paper, we study a food chain chemostat model with Michaelis-Menten function response and double delays. Applying the stability theory of functional differential equations, we discuss the conditions for the stability of three equilibria, respectively. Furthermore, we analyze the sufficient conditions for the Hopf bifurcation of the system at the positive equilibrium. Finally, we present some numerical examples to verify the correctness of the theoretical analysis and give some valuable conclusions and further discussions at the end of the paper.
- chemostat model,
- delay,
- equilibrium,
- stability,
- Hopf bifurcation
Citation: Xin Xu, Yanhong Qiu, Xingzhi Chen, Hailan Zhang, Zhiyuan Liang, Baodan Tian. Bifurcation analysis of a food chain chemostat model with Michaelis-Menten functional response and double delays[J]. AIMS Mathematics, 2022, 7(7): 12154-12176. doi: 10.3934/math.2022676

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Abstract

In this paper, we study a food chain chemostat model with Michaelis-Menten function response and double delays. Applying the stability theory of functional differential equations, we discuss the conditions for the stability of three equilibria, respectively. Furthermore, we analyze the sufficient conditions for the Hopf bifurcation of the system at the positive equilibrium. Finally, we present some numerical examples to verify the correctness of the theoretical analysis and give some valuable conclusions and further discussions at the end of the paper.

References

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