Open AccessBifurcation and control of a predator-prey system with unfixed functional responses
Author(s) -
Lizhi Fei,
Xingwu Chen
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021292
Subject(s) - mathematics , bifurcation , correctness , function (biology) , predation , discrete mathematics , algorithm , biology , physics , nonlinear system , paleontology , quantum mechanics , evolutionary biology
In this paper we investigate a discrete-time predator-prey system with not only some constant parameters but also unfixed functional responses including growth rate function of prey, conversion factor function and predation probability function. We prove that the maximal number of fixed points is \begin{document}$ 3 $\end{document} and give necessary and sufficient conditions of exactly \begin{document}$ j $\end{document} ( \begin{document}$ j = 1,2,3 $\end{document} ) fixed points, respectively. For transcritical bifurcation and Neimark-Sacker bifurcation, we provide bifurcation conditions depending on these unfixed functional responses. In order to regulate the stability of this biological system, a hybrid control strategy is used to control the Neimark-Sacker bifurcation. Finally, we apply our main results to some examples and carry out numerical simulations for each example to verify the correctness of our theoretical analysis.