带有食饵趋向和非单调反应函数捕食模型的稳定性及Hopf分支  

Stability and Hopf Bifurcation for a Predator-prey Model with Prey-taxis and Non-monotonic Functional Response

作　　者：李成林[1,2] 

机构地区：[1]西南大学数学与统计学院 [2]保山学院数学学院

出　　处：《北华大学学报（自然科学版）》2011年第5期505-510,共6页Journal of Beihua University（Natural Science）

基　　金：教育部自然科学基金资助项目(20100182110003)

摘　　要：探讨了一类在齐次留曼边界条件下带有捕食趋向和非单调反应函数捕食模型的稳定性及Hopf分支.证明了在一定条件下当食饵趋向系数充分小时正常数解是全局渐近稳定的,但局部稳定性及其他常数解全局稳定性与食饵趋向系数无关,并证明了该模型有周期解分支.A predator-prey model with prey-taxis incorporating non-monotonic functional response under homogeneous Neumann boundary condition is concerned.The stability and Hopf bifurcation of positive equilibrium points are investigated.The global stability of the positive constant solution is relative to prey-tactic sensitivity coefficient which leads to keep back the global stability,but for the local stability and the global stability of other constant solution,prey-tactic sensitivity coefficient doesn＇t influence on it,and above system has also the periodic bifurcation.

关 键 词：食饵趋向 稳定 HOPF分支 

分 类 号：O175.1[理学—数学]