Abstract: The predator-prey model with non-monotonic function is studied. The two growth rates are treated as corresponding bifurcation parameters, the bifurcation from a double eigenvalue is investigated by Liapunov-Schmidt procedure. The stability of these solutions is determined. Coexistence equilibrium can be reached between two species of prey and predator near trivial solution （0，0）.

Key words: predator-prey model, bifurcation solution, consistently stability

摘要： 研究一类具有非单调功能函数的捕食-食饵模型，以物种的生长率作为分歧参数，利用Lyapunov-Schmidt约化过程，研究二重特征值处的分歧，并判定分歧解的渐近稳定性。说明捕食与被捕食的两种生物在平凡解[(0,0)]附近可以产生稳定的共存状态。

关键词: 捕食-食饵模型, 分歧解, 渐近稳定性