Wu Characteristic Set Method For Solving The Discrete Lotka-volterra Predator - Prey Competition System

Wu characteristic set method which is first proposed by the famous Chinese mathematician Wu wenjun is the core algorithm of his theory of mathematics mech-anization, the mechanical proving methods and equations solving methods are both based on this. Algebraic and differential characteristic set methods have more ma-ture theories. But the difference characteristic set method has been developed by Gao xiaoshan and others recently. They proved the difference Wu-Ritt zero decom-position theorem and proposed the difference characteristic set algorithm. And the difference characteristic set algorithms have been applied in certain areas:such as, under these algorithms, we can solve the problems of determination triviality of the difference polynomial systems, equivalently, determine if a difference polynomial an-nuals in the zeros of a set of polynomials; the algorithms also solve the membership problem of perfect difference ideals, and also we have applied the algorithms in the mechanical proving some classes of difference theorems.The contents of this paper is to give an application of the algorithm based on the difference characteristic set method which is proposed by Gao xiaoshan, Luoyong and others, that is, under the algorithm, we give the symbolic solutions of some models of biological species. In this paper, we set the Lotka-Volterra predator-prey system as an example. We give the symbolic solutions using the difference characteristic set algorithms, analysis the symbolic solutions and their images, and we get a conclusion of that this type of biological species is not extinct.