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

Taking the third-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 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 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.For the necessity of the research, the global asymptotic stability criteria for the general autonomous delay differential equations are proved.3.Two kinds of third-order delay differential equations are studied and some sufficient conditions for the asymptotic stability and global asymptotic stability of the zero solution of them are reached respectively.4.Two kinds of third-order differential equations with two delays are studied and some sufficient conditions for the global asymptotic stability of the zero solution of them are set up.Then the numerical simulation is carried out through Matlab so as to validate the effectiveness of the obtained results.