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

AIMS Mathematics

Zhiyuan Liang¹  Baodan Tian¹  Hailan Zhang¹  Yanhong Qiu¹  Xin Xu¹  Xingzhi Chen² 

[1] 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;

关键词: chemostat model;    delay;    equilibrium;    stability;    hopf bifurcation;   

DOI  :  10.3934/math.2022676

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown