To discuss a type of reaction diffusion system with functional reaction and periodic coefficients.The existence and stability of periodic solution are studied by using the bifurcation theory,linear stability theory and the method of asymptotic expansion.

• 讨论具有功能反应的一类捕食者-食饵系统的反应扩散方程组.；运用分歧理论、固有值的解析摄动理论和渐近展开的方法；获得了共存时间周期解的存在性和稳定性