With Almost Periodic Solutions For Delay Ecosystem

The persistence, stability and the existence of positive almost periodic solutions of an ecological system is an important direction of mathematical ecology reserch. It has been an important topic to give a definite criterion of these upper properties of a complicated Lotka-Volterra system, and many scholars have paid more attention to this field.For ecological system, The state of the system in a moment will be influenced by the state in history as well as by the relation of species at that moment, say, the influence of time delay, and so if we consider it, we will be more precisely in discribe the change and development of the system; On the other hand, the population of species may be distributed in different patchs because of the influences of envionment or artificial element, this made us had to consider not only the time element but also the spatial element, said the diffusion of species. The theoretical works on this problem were pioneered by Skellam,and Levin prompted it. However, it's seemed that the research result of diffusionmodel in an almost periodic environment is rare to appear.This paper mainly study the uniformly persistence and the properties of almost periodic solution for a kind of competitive system with diffusion and time delay. We obtain the sufficient conditions for globally asymptotically stable of the system. We organized the whole paper as follow:In section 1, we introduce the background of this article in brief and give out the improved model and do some prepare works; In section 2, we will prove the system is uniformly persistant under some conditions; In section 3, we will prove the system is globally asymptotically stable by using Lyapuvov function; In section 4, we will give sufficient conditions of the existence, uniquness and global asymptotical stability of positive almost periodic, solutin of the almost, periodic system.