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Research Article | Open Access

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

Xin Xu1, Yanhong Qiu1( ), Xingzhi Chen2, Hailan Zhang1, Zhiyuan Liang1, Baodan Tian1( )
College of Mathematics and Physics, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
College of Mathematics and Statistics, Chongqing University, Chongqing 400000, China
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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.

Keywords

chemostat modeldelayequilibriumstabilityHopf bifurcation
CLC number: 34D05, 37N25, 92B05

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12154-12176
DOI: 10.3934/math.2022676

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Cite this article:
Xu X, Qiu Y, Chen X, et al. Bifurcation analysis of a food chain chemostat model with Michaelis-Menten functional response and double delays. AIMS Mathematics, 2022, 7(7): 12154-12176. https://doi.org/10.3934/math.2022676

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Received: 11 February 2022
Revised: 04 April 2022
Accepted: 13 April 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)