Periodic Solutions And Structural Stability Of Ordinary Differential Equations

The ordinary differential equation is a highly theoretical and widely applied math-ematics subject.The stability of the dynamic system and the periodic solution of the differential equation are the main research parts of the ordinary differential equation.The study of the structural stability of power system is the influence of disturbance fac-tors on the original system.The periodic solution of differential equations describes the changing laws of nature by exploring the periodicity of the time solution.In view of the above two aspects,this paper is divided into two parts.Part ?(Chapter 3),we use the idea of Hartman theorem to prove the relationship between the nonlinear dynamic system x = f(x),x ? Rn,and the flow of its perturbation system x = f(x)+ ?(x),x ? Rn.and explain that the original system is stable when the disturbance term ? is small enough.Correction of the relevant evidence in document[2].Part ?(Chapter 4),By using the knowledge of limit cycles,we prove the existence,uniqueness and stability of periodic solutions for a class of ordinary differential systems.x + f(x)x + g(x)= 0.