Open AccessBifurcation analysis of a food chain chemostat model with Michaelis-Menten functional response and double delays
Author(s) -
Xin Xu,
Yu Qiu,
Xingzhi Chen,
Hailan Zhang,
Qinxin Zhao,
Baodan Tian
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022676
Subject(s) - chemostat , correctness , hopf bifurcation , bifurcation , mathematics , stability (learning theory) , functional response , chain (unit) , function (biology) , food chain , control theory (sociology) , computer science , biology , physics , ecology , algorithm , genetics , predation , control (management) , nonlinear system , quantum mechanics , machine learning , astronomy , artificial intelligence , bacteria , predator
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.