Open AccessStability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting
Author(s) -
Ming Liu,
Dongpo Hu,
Fanwei Meng
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020259
Subject(s) - center manifold , mathematics , hopf bifurcation , bifurcation , stability (learning theory) , functional response , type (biology) , predator , mathematical analysis , control theory (sociology) , predation , nonlinear system , physics , computer science , biology , ecology , control (management) , quantum mechanics , machine learning , artificial intelligence
The present paper considers a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. The existence of the nontrivial positive equilibria is discussed, and some sufficient conditions for locally asymptotically stability of one of the positive equilibria are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delays as the bifurcation parameters. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out to support the analytical results.