Massera-Type theorem and asymptotically periodic Logistic equations☆

Some important properties of asymptotically periodic functions were studied in this paper. Sufficient conditions of existence of globally stable asymptotically periodic solution were obtained. Then, Massera-Type theorems were discussed for one-dimensional, two-dimensional, higher-dimensional asymptotically periodic systems. Finally, global stability of periodic Logistic equations and asymptotically periodic Logistic equations were considered, respectively.