一类捕食模型正平衡解的局部分歧及稳定性

The local bifurcation and stability of positive steady-state solutins for a class of predator-prey model

目的讨论一类捕食-食饵生态模型的平衡态系统在第一边界条件(或者是第三边界条件)下,分歧解的存在性和稳定性。方法局部分歧及其稳定性理论,线性化算子的扰动理论。结果在半平凡解(aθ,0)处存在正解分歧,且分歧解稳定。结论推广了模型多解的条件。

Aim To study the existence and stability on one kind of bifurcation solutions of steady-state system for a class of predator-prey biological system under the first boundary condition（or the third boundary condition）.Methods Using the local bifucation and stability therories and the perturbation theorem for linear operator.Results The existence and the stability for the system generates bifurcation at semi-trivial solutions（θa,0）.Conclusion The conditions of multiresolution are expended.