高阶非线性非自治系统分析研究

为了更有效的解决高阶非线性非自治系统的求解问题,提出基于等效小参数法的高阶非线性非自治系统的求解方法,应用分解法原理,通过引入谐波平衡和同阶小量相等,建立一类非线性动态系统周期解的逆算符表达的递推算法,将高阶非线性非自治系统转化成一个通用方程,然后利用Matlab开发出相应的软件系统,实现计算机自动求解。对包含sin（t）或cos（t）的非线性非自治GENESIO系统和非线性非自治COULLET系统使用等效小参数法进行详细推导,分别求解非自治GENESIO系统和非自治COULLET系统的周期解,该算法具有较高的计算精度和较大的普适性,是求解一类非线性非自治系统周期解的有效方法。

Study and Analysis on High Order Nonlinear Nonautonomous System

A solution based on equivalent parameter method for the high order non-autonomous non-linear system is proposed in this paper. Guided by the principle of decomposition method, harmonic balance and same-order small amount equality is introduced in this proposed method, a class of recurrence algorithm expressed by inverse operators of periodic solutions to non-linear dynamic systems is set up, and the high order non-linear non-autonomous system is converted to currency equation, then computer automatic solving is implemented by using corresponding software systems deve]oped with Matlab. The comparison shows that the algorithm is of higher calculation precision and greater universality and is an effective solution method for periodic solutions to high-order non-linear non-autonomous systems.