非线性动力系统标准化问题的研究

Research on the standardization of nonlinear dynamical system

提供了高效、简捷的将高维非线性动力系统标准化(化为状态变量的多项式)的实现方法.文中使用计算机代数系统Mathematica编写了程序模块,提供了具有通用性的程序;程序模块在将系统标准化的同时,把各阶齐次项顺序给出,为计算系统的中心流形、Normal-Form等工作提供了方便,进而为研究动力系统的性态奠定了基础.并举例说明了程序的应用.

In this paper an efficient and simple method is presented on calculating the standard form (polynomials of state variables)of nonlinear dynamical system. Using computer algebra Mathematica we have composed the universal program that can finish the task above swiftly. With generating the standard form, the program also presents the terms of all orders, and makes it easy to finish the further tasks on studying the nonlinear dynamical system. The examples are given in order to show the efficiency of the program.