带有避难所的捕食-食饵模型的稳定性Neimark-Sacker分支  

Stability and Neimark-Sacker Bifurcation Behavior of Predator-Prey Model with Refuge

作　　者：豆中丽[1] 王锐[2] DOU Zhong-li;WANG Rui(Rongzhi College of Chongqing Technology and Business University,Chongqing 400055,China;School of Mathematics Science,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆工商大学融智学院,重庆400055 [2]重庆大学数学科学学院,重庆401331

出　　处：《数学的实践与认识》2019年第24期246-252,共7页Mathematics in Practice and Theory

基　　金：重庆市教委科技项目(KJQN201902105)

摘　　要：讨论了一类带有避难所的捕食-食饵模型的稳定性和Neimark-Sacker分支行为.首先通过计算得到该模型对应的差分方程,利用线性稳定性理论讨论平衡点的局部渐近稳定性;其次运用正规形理论和中心流形投影法阐释了系统随参数变化而发生翻转分支和Neimark-Sacker分支进入混沌的情形;最后进行数值模拟验证研究理论结果的正确性.A kind of predator-prey model with refuge was approached.Stability and Neimark-Sacker bifurcation behavior property of the model were discussed detailedly.The difference equation corresponding to this kind of model was obtained at first by function transformation.And the sufficient condition of the positive equilibrium's local asymptotic stability was derived by the linear stability theory.Secondly,with parameter variation,normal form theory and center manifold projection method were used to deduce the cases of the system that caused flip bifurcation and Neimark-Sacker bifurcation into the chaos.In the last part,numerical simulations were experimented to verify the correction of the results approached in this paper.

关 键 词：分段常数变量 稳定性 捕食-食饵模型 Neimark-Sacker分支 

分 类 号：O175[理学—数学] Q141[理学—基础数学]