The existence of peoriodic solutions is given first, then the global attractivity of coupled system of semilinear parabolic equations is investigated by using upper and lower solutions and through principal eigenvalue analysis.

• 首先给出周期解的存在性，再用有序上下解及主特征值分析方法研究耦合半线性抛物方程组周期解的全局吸引性。