Globally asymptotic stability in two periodic delayed competitive systems

Based on two types of well known periodic single-species population growth models with time delay, we propose two corresponding periodic competitive systems with multiple delays. By using some new analysis techniques, we derive the same criteria for the existence and globally asymptotic stability of positive periodic solutions of the above two competitive systems. The easily verifiable criteria show that the existence and globally asymptotic stability of positive periodic solutions of two delayed nonautonomous competitive systems correspond to the existence and global stability of positive equilibrium of corresponding undelayed autonomous system. As an application, some special cases of the above systems are examined and some earlier results are extended and improved. Biological interpretations on the main results are also given.