关键词: 互惠系统； 多时滞； 正周期解； 重合度理论

Abstract:

We studied the existence of positive periodic solutions for a nonautonomous cooperative system with discrete time and several de
lays by means of the continuation theorem based on coincidence degree  theory. One bounded open set was obtained by virtue of  analytic technique. With the help of  the coincidence degree theory, a set of sufficient conditions for this system to have at least one positive periodic solution were obtained. The research result reveals the nonautonomous cooperative system with discrete time and several delays will produce periodic oscillation of biological nature, and the time delay is harmless.

Key words: cooperative system； several delays； positive periodic solution； coincidence degree theory