Open AccessHopf bifurcation in a delayed predator-prey system with asymmetric functional response and additional food
Author(s) -
Luoyi Wu,
Hang Zheng
Publication year - 2021
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.2021708
Subject(s) - functional response , center manifold , hopf bifurcation , mathematics , correctness , predation , stability (learning theory) , pitchfork bifurcation , bifurcation , period doubling bifurcation , saddle node bifurcation , control theory (sociology) , mathematical analysis , predator , physics , computer science , nonlinear system , biology , paleontology , control (management) , algorithm , quantum mechanics , machine learning , artificial intelligence
In this paper, a delayed predator-prey system with additional food and asymmetric functional response is investigated. We discuss the local stability of equilibria and the existence of local Hopf bifurcation under the influence of the time delay. By using the normal form theory and center manifold theorem, the explicit formulas which determine the properties of bifurcating periodic solutions are obtained. Further, we prove that global periodic solutions exist after the second critical value of delay via Wu's theory. Finally, the correctness of the previous theoretical analysis is demonstrated by some numerical cases.