Studies On The Stability Of Solutions For Several Kinds Of Delay Differential Equations

Taking the third-order and fourth-order delay differential equations as the subject, by the second method of Lyapunov, this paper mainly focuses on the asymptotic stability or global asymptotic stability of the zero solution of several kinds of third-order and fourth-order delay differential equations, and some sufficient conditions for the asymptotic stability or global asymptotic stability of the trivial solution of them are established. The main content is depicted as follows:1. The background and significance of the stability of delay differential equations are explained and the research status of third-order and fourth-order delay differential equations is presented. Based on this, the content of this study is introduced.2. The concept of delay differential equations, the definition of stability, the method of Lyapunov functional and the Lyapunov functional of autonomous delay differential system are briefly introduced, which constitutes the theoretical basis of this study.3. (1) Two kinds of third-order delay differential equations are studied. The equation is studied by Cemil Tune such equation asOn the basis of the previous equation, the equation is studied which replaces (?) with (?) such equation asThe other equation is studied which replaces single time-delay with double-delay such equation asFinally some sufficient conditions for the global asymptotic stability of the zero solution of them are reached respectively.(2) Two kinds of fourth-order delay differential equations are studied. The equation is studied by Sadek such equation asOn the basis of the previous equation, the equation is studied which replaces (?) with (?) and adds g[x(t-r),x(t-r)] such equation as The other equation is made to improve which replaces constant delay with variable delay and replaces (?) with (?) such equation asFinally some sufficient conditions for the asymptotic stability of the zero solution of them are reached.