Bifurcations,chaos analysis and control in a discrete predator-prey model with mixed functional responses  

作　　者：Yajie Sun Ming Zhao Yunfei Du 

机构地区：[1]School of Science,China University of Geosciences(Beijing)Beijing,100083,P.R.China [2]School of Basic Education Beijing Institute of Graphic Communication,Beijing,102600,P.R.China

出　　处：《International Journal of Biomathematics》2024年第3期185-210,共26页生物数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12001503);the Project of Beijing Municipal Commission of Education(KM 202110015001)。

摘　　要：Many discrete systems have more distinctive dynamical behaviors compared to continuous ones,which has led lots of researchers to investigate them.The discrete predatorprey model with two different functional responses(Holling type I and II functional responses)is discussed in this paper,which depicts a complex population relationship.The local dynamical behaviors of the interior fixed point of this system are studied.The detailed analysis reveals this system undergoes flip bifurcation and Neimark-Sacker bifurcation.Especially,we prove the existence of Marotto's chaos by analytical method.In addition,the hybrid control method is applied to control the chaos of this system.Numerical simulations are presented to support our research and demonstrate new dynamical behaviors,such as period-10,19,29,39,48 orbits and chaos in the sense of Li-Yorke.

关 键 词：Predator-prey model flip bifurcation Neimark-Sacker bifurcation Marotto's chaos chaos control 

分 类 号：O17[理学—数学]