一般的Gause型捕食-食饵模型的定性分析

Qualitative analysis for a general Gause-type predator-prey model

研究了带有非齐次Dirichlet边界条件的一般的Gause型捕食-食饵模型.分析了正常数解的局部及全局渐近稳定性;在给出平衡解先验估计的基础上,研究了非常数非负平衡解的不存在性条件,证明了当两物种u、v的扩散系数d1和d2都比较大时,平衡态系统不产生空间非均匀的解形态;以捕食者的扩散系数d2为分歧参数,利用度理论和分歧理论,得到此平衡态系统正解的存在性.

A general Gause-type predator-prey model with non-homogeneous Dirichlet boundary condition is investigated. The local and global stable conditions of the positive constant solution are given. Based on priori estimates,non-existence of non-constant nonnegative steady-states is discussed,it is proved that the steady-state system cannot create non-homogeneous spatial structure when the diffusion coefficients are enough large.By using degree theory and global bifurcation theorem,the existence of positive steady-state solutions is proved.