【摘要】 研究了一类具有Holling-Ⅲ型功能性响应函数的捕食模型.首先证明常数平衡解的稳定性,然后给出了平衡态问题正解的先验估计,以及非常数正解的不存在性,最后利用计算拓扑度的方法得到了平衡态问题的非常数正平衡解的存在性.更多还原

【Abstract】 A predator-prey system with Holling type Ⅲ functional response under homogeneous Neumann boundary condition is considered. Firstly,we study the globally asymptotically stability of semi-trivial solution and locally asymptotically stability of the positive steady-states to the system. Secondly,a priori estimates (positive upper and lower bounders) and the sufficient condition of the non-existence of non-constant positive steady-states are given. Finally,we establish the existence of non-constant positive steady-states for the elliptic system by using topological degree.更多还原