中文摘要：

研究带交叉扩散项的Holling Ⅳ捕食-食饵模型在齐次Dirichlet边界条件下正解的存在性及其局部分歧.利用极大值原理得到正解的先验估计;通过分析相关特征值问题,得到两条无界的中性曲线;借助分歧理论,得到发自半平凡分支（a^＊;θa^＊^-,0）和（a^＊;0,θb^-）的局部分歧正解.

英文摘要：

The paper discusses the existence of positive solutions to a Holling IV predator-prey model with cross-diffusion under the homogeneous Dirichlet boundary conditions and their local bifurcation. By the maximum principle, the priori estimate of positive solutions is obtained. Then, by analyzing the related eigenvalue problems, two unbounded neutral curves are obtained. Finally, by using the bifurcation theory, the local bifurcation positive solutions to （a^＊;θa^＊^-,0）and （a^＊;0,θb^-） from half ordinary branch are determined.