Dynamics of a discrete predator-prey model with Holling-II functional response  

作　　者：Yuqing Liu Xianyi Li 

机构地区：[1]Department of Big Data Science,School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,P.R.China

出　　处：《International Journal of Biomathematics》2021年第8期253-272,共20页生物数学学报（英文版）

基　　金：This work is partly supported by the National Natural Science Foundation of China(61473340);the Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province;the National Natural Science Foundation of Zhejiang University of Science and Technology(F701108G14).

摘　　要：In this paper,we use a semidiscretization method to derive a discrete predator–prey model with Holling type II,whose continuous version is stated in[F.Wu and Y.J.Jiao,Stability and Hopf bifurcation of a predator-prey model,Bound.Value Probl.129(2019)1–11].First,the existence and local stability of fixed points of the system are investigated by employing a key lemma.Then we obtain the sufficient conditions for the occurrence of the transcritical bifurcation and Neimark–Sacker bifurcation and the stability of the closed orbits bifurcated by using the Center Manifold theorem and bifurcation theory.Finally,we present numerical simulations to verify corresponding theoretical results and reveal some new dynamics.

关 键 词：Discrete predator-prey system semidiscretization method transcritical bifurcation Neimark-Sacker bifurcation 

分 类 号：O17[理学—数学]