一类非线性动力系统实用稳定域的研究及应用

借助于李雅普诺夫函数讨论了一类非线性动力系统的实用稳定性和实用稳定域的估计问题,得到了实用稳定域存在的充分条件,给出了一类动力系统实用稳定域的具体形式.通过具体实例说明了所给条件的实用性,改进了已有的结果.     

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FIFTH ORDER DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＢＯＵＮＤＥＤＮＥＳＳＡＮＤＴＨＥＳＴＡＢＩＬＩＴＹＲＥＳＵＬＴＳＦＯＲＴＨＥＳＯＬＵＴＩＯＮＯＦＣＥＲＴＡＩＮＦＩＦＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＣＥＭＩＬＴＵＮＣ（ＹｕｚｕｎｃｕＹｉｌＵｎｉｖｅｒｓｉｔｙ，Ｅｇ...     

一类具有两个非线性控制项的系统绝对稳定的充要性条件

本文给出一类具有两个非线性控制项的系统绝对稳定的充要性判据.该判据关于未定常数均是线性的,易于检验,且有较广适用范围.     

Simple Equations Method and Non-Linear Differential Equations with Non-Polynomial Non-Linearity

We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate transformation at Step (1.) of SEsM. This transformation has to convert the non-polynomial non- linearity to polynomial non-linearity. Then, an appropriate solution is constructed. This solution is a composite function of solutions of more simple equations. The application of the solution reduces the differential equation to a system of non-linear algebraic equations. We list 10 possible appropriate transformations. Two examples for the application of the methodology are presented. In the first example, we obtain kink and anti- kink solutions of the solved equation. The second example illustrates another point of the study. The point is as follows. In some cases, the simple equations used in SEsM do not have solutions expressed by elementary functions or by the frequently used special functions. In such cases, we can use a special function, which is the solution of an appropriate ordinary differential equation, containing polynomial non-linearity. Specific cases of the use of this function are presented in the second example.