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

AIMS Mathematics

article

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

[1] College of Mathematics and Physics, Southwest University of Science and Technology;College of Mathematics and Statistics, Chongqing University

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

DOI  :  10.3934/math.2022676

学科分类：地球科学(综合)

来源: AIMS Press

【 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】

CC BY