Existence and Stability of Periodic Solution for Periodic Logistic System with Periodic Impulsive Perturbations

This paper studies the existence and stability of periodic PC-mild solution for the omega-periodic logistic system with T₀ -periodic impulsive perturbations on Banach spaces. One sufficient condition with gamma = omega/T₀ is rational that guarantees the exponential stability of the impulsive evolution operator which is given. It is shown that the system has a unique periodic PC-mild solution which is globally asymptotically stable when omega and T₀ are rational dependent and its period must be nT₀ for some n isin N. At last, a numerical example is given for demonstration.