In this paper, we are concerned with the species interaction model with the ratio-dependent Holling III functional response and strong Allee effect. To explore nonhomogeneous solutions of the model, we consider the existence and non-existence of non-constant steady states and temporal bifurcation. Then we show the boundedness of the global positive solutions for the parabolic system and present the upper and lower bounds of positive solutions for the associated elliptic system. The non-existence and existence of the non-constant steady states of the elliptic system with the homogeneous Neumann boundary conditions are obtained by using the priori estimates, maximum principle and index theory. Furthermore, the existence and the direction of Hopf bifurcation are investigated via the stability analysis, center manifold theory and normal form reduction. Numerical simulations are carried out to verify our theoretical analysis and to illustrate that the ratio-dependent Holling III functional response and strong Allee effect have strong impact on dynamical behaviors of the species interaction systems.

在本文中，我们关注具有比率依赖的 Holling III 功能响应和强 Allee 效应的物种相互作用模型。为了探索模型的非齐次解，我们考虑了非常量稳态和时间分岔的存在和不存在。然后我们展示了抛物线系统的全局正解的有界性，并给出了相关椭圆系统的正解的上限和下限。利用先验估计、极大值原理和指数理论，得到了齐次Neumann边界条件下椭圆系统非定常稳态的不存在与存在。此外，通过稳定性分析、中心流形理论和范式约简研究了Hopf分岔的存在和方向。