中文摘要：

本文研究了在有界区域上带有Neumann边界条件的反应扩散三物种食饵．捕食时滞系统．利用特征值方法和Lyapunov函数找到了该系统平衡点稳定的充分条件，该条件说明时滞限制了稳定性．稳定性中的主要一个结论是当食饵和捕食者间的种内竞争大于种间竞争时正平衡点是全局渐近稳定的．进一步，通过构建上下解证明了当波速相对大时该系统具有连接零平衡点和正平衡点的行波解．

英文摘要：

This paper is concerned with a three-species delayed reaction-diffusion predator- prey system in a bounded domain with Neumann boundary condition. The suffi- cient conditions of stability are found for equilibria of this system by the method of eigenvalue and Lyapunov function, and these conditions imply that delays often restrain stability. One of the main results about stabilities shows that if the intra- specific competitions of the predator and preys dominate their inter-specific inter- action, then the positive equilibria are globally stable. Furthermore, the existence of the traveling wavefront is considered by constructing upper-lower solution and it is derived that this system always has a traveling wave solution connecting the trivial steady state and the positive steady state when the wave speed is relatively big.