一种改进的不变流形算法  

An improved algorithm of computing invariant manifolds

作　　者：郭克敏[1] 李清都[1] 

机构地区：[1]重庆邮电大学非线性系统研究所,重庆400065

出　　处：《重庆邮电大学学报（自然科学版）》2008年第2期221-224,共4页Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)

基　　金：国家自然科学基金资助(10672062)

摘　　要：不变流形在动力学研究的许多方面都有重要意义,由于不变流形很难通过解析表达式求解,对其做近似计算就成为重要的手段。介绍了一种改进的流形计算算法,该算法由两步构成:首先利用PDE算法在不变流形上求出一些均匀的点;再借助三角形剖分方法利用PDE算法算出的点画出直观流形图。该算法避免了频繁求解微分方程问题,没有求解多余的轨道,且求解的精度也容易控制,得到的流形图直观。Invariant manifolds are important for the study of dynamic systems. Since they are hard to be computed by analytical expression, the numerical method for approximating invariant manifold is an important mean. An improved algorithm is proposed, which consists of two steps： First, to calculate points in the unstable manifold by PDE algorithm; secondly, to draw picture of the manifold with these points by means of triangle partition. This algorithm avoids solving differential equation frequently as well as redundant orbit, and it is easy to control the accuracy and to get the picture of manifold.

关 键 词：流形计算 稳定流形 不稳定流形 动力学系统 神经网络 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]