The Positive Periodic Solutions Of N-dimensional Periodic Population Dynamical Systems With Impulse

Since impulsive population dynamic systems have enormous potential in wide vari-eties of applications, many specialists and scholars apply themselves to the research of thetheory and achieve many perfect productions. In this paper, we perform researches of theexistence of positive periodic solutions for impulsive population dynamic systems. Themain contents of this paper include: the existence of positive periodic solutions for a gen-eral periodic system with delay and impulse and its some applications on single populationsystem, Lotka?V olterra competitive system, predator-prey system and Lotka?V olterratwo competitive system with dispersion in n pathes.The main contents in this paper can be summarized as follows:1. Firstly, in the first section, we introduce the developmental process and significanceof impulsive population dynamic systems. Then we introduce the research results for theexistence of periodic solutions for impulsive population dynamic systems. Finally theorganization of this paper is given.2. In the second section, the existence of positive periodic solutions for a generalperiodic system with delay and impulse is studied. Based on Horn s fixed point theoremof Banach spaces, some su?cient conditions for the existence of positive periodic solutionsfor such a system are obtained.3. In the third section, the existence of positive periodic solutions for impulsivesingle population system, Lotka?V olterra competitive system, predator-prey system andLotka?V olterra two competitive system with dispersion in n pathes are discussed. Somenew su?cient conditions which include the existence of positive periodic solutions areobtained by using comparison principle for impulsive di?erential equations and inequalitytechniques.4. In the forth section, some numerical examples are given to show the existence ofthe positive periodic solutions.