中文摘要：

研究了一类周期差分抛物系统时间周期解的存在性、稳定性和吸引性.所考虑的问题包含抛物型方程和常微分方程构成的方程组,时滞可能出现在非线性反应函数和边界条件中.当反应函数和边界条件为局部Lipschitz连续时,利用Brower不动点定理,得到时间周期解的存在性;进一步,当反应函数和边界条件为拟单调时,利用单调迭代方法得到了时间周期解的稳定性和吸引性.

英文摘要：

The existence, stability, and attractivity of time-periodic solutions for a class of coupled parabolic difference equations in a bounded domain are concerned. A system of parabolic equations and ordinary differential equations is taken into consideration. Time delays may occur in non-linear reaction functions and boundary conditions. By using Brower＇s fixed point theorem we get the existence of time-periodic solutions for a class of locally Lipschitz continuous reaction functions and boundary conditions without any quasimonotone requirement. Meanwhile, by using the monotone iterative scheme we get the stability and attractivity for quasimonotone reaction functions and boundary conditions.