N +1 Dimensional Non-autonomous Predator - Prey System Of Coexistence

The problem about coexistence of ecological system and the existence of positive periodic solutions is an important part of mathematical ecology. It is an important topic to study the coexistence of nonautonomous predator-prey system and give a definite criterion. Many scholars have paid more attention to it which has good prospects in practical application.In this paper,we mainly study coexistence problem of nonautonomous predator-prey system with n-predator and one-prey, and study the existence of positive periodic solutions when the coefficients are periodic functions. We derive sufficient conditions for coexistence by carefully analysising right functions of system which is different from Liapunov second method. This paper prodives some information about above theory and enrich it.The article is organized as follows:In section 1, we introduce preface. In section 2, we make some preparations for next setion. In section 3, we study the coexistence of the system and derive sufficient conditions of the system and some important corollaries. In setion 4, we prove the existence of positive periodic solutions by the fixed point theory.