一类基于比率和带收获率的捕食模型解的性质  

Properties of Solutions for a Ratio-dependent Predator-prey System with Harvesting Rate

作　　者：刘清[1] 李艳玲[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《河北师范大学学报（自然科学版）》2013年第2期119-124,共6页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(10971124);教育部高等学校博士点专项基金(200807180004)

摘　　要：研究了一类具有扩散项和按比例收获的捕食-食饵模型在齐次Neumann边界条件下解的性质.首先利用比较原理讨论了解的耗散性,其次应用特征值理论得到了正常数平衡解的稳定性,然后运用局部分歧理论得到了在N维情形下正常数平衡解处产生的局部分歧,给出了分歧点附近解的结构,最后使用全局分歧理论证明了局部分歧可以延拓成全局分歧.Qualitative properties of solutions for predator-prey model with diffusion and ratio-dependent harvesting subject to the homogeneous Neumann boundary condition is studied. The dissipation of solutions by using the comparison principle is discussed;the stability of positive constant steady-state solution by using eigen value theory is obtained;for N-dimensional case the local bifurcation at positive constant steady-state solution is shown by local bifurcation theory and the structure of solutions near bifurcation point is given. Finally,the local branch can be extended to the global branch by global bifurcation theory.

关 键 词：捕食-食饵模型 平衡解 稳定性 分歧 

分 类 号：O175.26[理学—数学]