一类带有饱和与竞争项捕食模型解的线性稳定性

Linear Stability of Solutions of a Predator-Prey Model with Predator Saturation and Competition Function

将一类边界条件为Neumann边界、带有饱和与竞争项的捕食模型转化为非负常稳态解的线性化方程,该线性方程方程所对应的矩阵的特征值的实部都是负的,进而确定该模型非负常稳态解是线性稳定的,并得到模型非负常稳态解的存在性和线性稳定性的充分条件是0<k<a/(1+ab)和ab<kc(1+ab).

We linearizes a class of predator-prey model at the nonnegative constant steady states solutions, which has saturation and competition functional response under homogeneous Neumann boundary conditions, the eigenvalues of the corresponding matrix on the linearization equation have negative real parts, and then ensure that the nonnegative constant steady states solutions is linearly stable, and obtain the sufficient conditions： 0 〈 k 〈 a / （1 ＋ ab） and ab 〈 kc（1 ＋ ab） of existence and linear stability of the nonnegative constant steady states solutions of model.