一类高阶非线性动态系统周期解的逆算符表达

基于等效小参数法基本思想，应用分解法原理，通过引入逆算符和选择合适的线性与非线性算子，建立了一类非线性动态系统周期解的逆算符表达的递推算法，并利用Mathematica计算机代数语言开发出相应的软件系统，实现了该算法的计算机自动求解。利用该软件系统，可方便快速地求出周期解的解析表达式。文中给出了计算实例，并将算法所得结果与四阶Runge—Kutta数值方法的计算结果作了比较。理论和实例计算结果表明，该软件系统通用性强、精度高，是进行某类非线性动太民电路分析和计算的有力工具。

Inverse Operator Expression of Periodic Solutions for the High Order Nonlinear Dynamic Systems

In this thesis, based on the principle of the equivalent parameter method and applied the decomposition method, the inverse operator expression of the periodic solutions of some type high order nonlinear dynamic systems is given by inducting the athwart factor and selecting the appropritae linear and nonlinear factors. The automatic calculation of this arithmetic is realized by computer program that is based on Mathematica algebraic language. The example of practical calculation is also given and the calculated numerical results from this method are compared with those from the Runge Kutta method. Theory and calculating result reveals that the program has advantage of high accuracy and wide application, so it is an effective tool to calculate and analysis some type nonlinear dynamic circuits.