Applications Of Computer Algebra System To The Study Of Differential Equation

Differential equations have wide applications in many fields. Studying differential equations by mathematical software has boundless prospects. Maple computer algebra system is one of the excellent mathematical softwares, whose important feature is powerful symbolic operation. Maple has packages which contains functions and statements that help us work with differential equations very well. In addition, Users can program by themselves to extend Maple's function because its original program code is written by C-language and Maple has its own a set of programing language.Distinguishing weak focus and center point, determining stability of solution, the method of central manifold and Hopf bifurcation, the theory of normal form are important issues in the study of differential equation and dynamical system. This thesis presents computer programs about them by Maple which extend and simplify the achievements acquired by other researchers owe to using the thought of programing by computer higher-level language to realize automatically in reasoning and calculating, which is the feature and advantage of this thesis.In the end, analyzing and calculating Hopf bifurcation of a three-dimension Volterra-ecosystem(where a > 0) is done with computer fully by using the given programs and control statements provided by Maple.