Almost Periodic Solutions For Several Of Lotka-Volterra Competition System

The fundamental value of biological mathematics embodied in that its originates from the reality and application in reality. The differential equation is a mathematical model from practical problems, it is a portrait of the relationship between the changes of things and the state. Many practical problems can be attributed to the almost periodic solutions of differential equations. Almost periodic phenomenon can more comprehensively reflect the changes of things, such as mechanical vibration, celestial mechanics, electric power system, economics, ecology etc. And the studying about the almost periodic phenomenon of is more practical than the periodic phenomenon, sometimes the former can explain the reality of life. In the process of development of ecological system, periodic solutions and almost periodic solutions attracted a lot of attention, and they have become an important topic in mathematical ecology.In the study of population dynamics and ecology, people had put forward many mathematical models, one of the most classical models of population dynamics is Lotka-Volterra system. Because of its theoretical and practical significance, the Lotka-Volterra system has been development rapidly. And the dynamic properties of Lotka-Volterra system and the extension of the model are the prolonged study for people dozens of years. This established theoretical method is the most basic research results of biological population model content.This paper is mainly on the Lotka-Volterra competition system and its extension model for the existence and global stability of almost periodic solutions of the problem are summarized. The first chapter mainly introduces the mathematical biology, history of almost periodic solutions and almost periodic solutions of Lotka-Volterra competitive system model.The second chapter mainly introduces the nonautonomous Lotka-Volterra competitive n-dimensional system model. the only sufficient condition for almost periodic solution is globally attractive. By constructing suitable Lyapunov function proved thatTheorem2.2.1If this system satisfies (H2)There is a positive constant α>0, so that then the system has a strictly pusitive almost periodic solution G(t)={u1(t),...,un(t)}, t∈R, whose module is contained in that of WhereThe third chapter mainly introduces the generalized model of Lotka-Volterra competition system model, it has a variety of group competition system feedback control.The almost periodic solutions are given using the Lyapunov function method to study the competition system. Given the multi-species competition system with feedback control of the sufficient conditions for global stability of the almost periodic solution.Theorem3.2.1For this system, if set up:(H1*)bi(t),ri(t), aij(t), cij(t), di(t), ei(t), fi(t) are almost periodic functions defined on(-∞,+∞),(H2*)aii1>0,ri1>0.m(bi(t))>0,m(ei(t))>0, (H3*)m(bi(t)-∑j=1,i≠j(?)aij(t)xj*(t)-di(t)ui*(t)). the system on R contain the only positive bounded solution If the following assumptions are also established,there are constants ωi,si,εi,δi,and so that then the unique existence almost periodic solution Y(t)of the system is global attracted.