具有Smith增长和羊群行为的捕食系统的Hopf分支  

Hopf Bifurcation of a Predator-prey System with Smith Growth and Herd Behavior

作　　者：韦婷 李杰梅 WEI Ting;LI Jiemei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《江苏海洋大学学报（自然科学版）》2021年第3期88-93,共6页Journal of Jiangsu Ocean University:Natural Science Edition

基　　金：甘肃省教育厅高等学校创新能力提升项目(2019B-054);国家自然科学基金资助项目(11801243)。

摘　　要：研究了一类具有羊群行为且食饵为Smith增长的捕食者食饵模型。首先讨论了唯一正常数平衡点的局部渐近稳定性和空间齐次Hopf分支的存在性;其次运用规范型理论和中心流形定理,分析了空间齐次Hopf分支的方向和稳定性。研究结果表明,当食饵的Smith增长率等于一个阈值时,模型将出现Hopf分支,由此产生的空间齐次Hopf分支的分支周期解在一定条件下是稳定的。数值模拟验证了理论结果。A predator-prey model with herd behavior and Smith growth of prey is studied.Firstly,the local asymptotic stability and the existence of the spatially homogeneous Hopf bifurcation for the unique constant positive equilibrium are discussed.Furthermore,the direction and the stability of the spatially homogeneous Hopf bifurcation are derived by means of the normal form method and the center manifold theorem.The results have showed that Hopf bifurcation will appear in the model when Smith growth rate of prey reaches a threshold.The bifurcating periodic solutions of the spatially homogeneous Hopf bifurcation are stable under some certain conditions.Numerical simulations are provided to verify the theoretical results.

关 键 词：Smith增长 羊群行为 规范型理论 中心流形定理 

分 类 号：O175.2[理学—数学]