Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 524945, 16 pages
doi:10.1155/2008/524945

Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces

Jinrong Wang1 , X. Xiang2 , W. Wei2 and Qian Chen4

1Department of Computer, College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, China
 2Department of Mathematics, College of Science, Guizhou University, Guiyang, Guizhou 550025, China
 4Department of Electronic Science, College of Electronic Science and Information Technology, Guizhou University, Guiyang, 550025, China

Abstract

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic Logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T-periodic system with time-varying generating operators and T0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when T and T0 are rational dependent and its period must be nT0 for some n∈N. At last, an example is given for demonstration.