摘要
研究一类具有Hlling-Ⅱ型功能性响应函数的捕食模型.首先证明当系数满足一定条件时,常微分方程组和偏微分方程组的唯一正常数平衡解的局部渐近稳定性,然后利用最大值原理和Harnack不等式得到椭圆型方程组正解的先验估计,最后利用能量方法证明了如果种群扩散率强时,则椭圆型方程组不存在非常数正解.
In this paper, a kind of predator-prey model with Holling- Ⅱ functional response is discussed. It is proved that the unique positive constant steady states for the ODE system and PDE system are locally asymptotical stable under some proper conditions for the coefficients. Then it establishes the prior estimates on positive solutions of the corresponding elliptic system by Harnack inequality and maximum principle. Using energy method, it establishes the non-existence of non-constant positive solutions of the elliptic system.
出处
《扬州大学学报（自然科学版）》
CAS
CSCD
2007年第4期26-30,共5页
Journal of Yangzhou University：Natural Science Edition
基金
江苏省自然科学基金资助项目(BK2006064)
关键词
捕食模型
局部稳定
非常数正解
predator-prey model
local stability
non-constant positive solution
