一类带恐惧效应的三物种食物链模型的分支分析  

Bifurcation analysis of a model of a three-species food chain with a fear effect

作　　者：王彩宇 常玉 陈晓楠 WANG CaiYu;CHANG Yu;CHEN XiaoNan(College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China)

机构地区：[1]北京化工大学数理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2021年第5期119-123,共5页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：国家自然科学基金(11771033)。

摘　　要：主要研究了恐惧效应对三物种食物链模型中分支动态的影响,运用中心流形定理和局部分支理论分析了Hopf分支、transcritical分支和saddle-node分支的存在性,并给出相应的数值模拟结果。研究结果表明,分支是种群发生失稳和周期性振荡的根本原因,从而揭示了恐惧效应是维持种群稳定的重要因素。We have investigated the influence of fear effect on bifurcation dynamics in a threespecies food chain model.The existence of Hopf bifurcation,saddlenode bifurcation and transcritical bifurcation were studied using the corresponding center manifolds and local bifurcation theory,and numerical simulation studies demonstrated various types of bifurcation.All these results indicate that bifurcation is the fundamental cause of population instability and periodic oscillations that occur,and that fear effects play an important role in maintaining population stability.

关 键 词：中心流形 HOPF分支 transcritical分支 saddle-node分支 恐惧效应 

分 类 号：O193[理学—数学]