一种二维不稳定流形的新算法及其应用  

A new algorithm for computation of two-dimensional unstable manifolds and its applications

作　　者：李清都[1] 杨晓松[1,2] 

机构地区：[1]重庆邮电大学系统科学研究中心非线性系统研究所,重庆400065 [2]华中科技大学数学系,武汉430074

出　　处：《物理学报》2010年第3期1416-1422,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10672062;10972082);重庆市教委项目(批准号:KJ080515);重庆市科委项目(批准号:CSTC-2008BB2409)资助的课题~~

摘　　要：提出了连续时间系统二维(不)稳定流形的一种新数值算法,不但可以快速地求得流形的直观图像,而且能够准确地获取流形上各点的位置、时间、轨道距离等丰富的信息,从而有利于人们从几何上去研究系统的全局行为,如边界特征、演化过程、奇异环等等.本算法首先通过解初值问题求出均匀分布的相邻轨道,然后连接这些轨道既得流形面.Lorenz系统原点的稳定流形的计算表明本算法快速有效.此外,通过试着寻找异宿轨道,还研究了一个三维神经网络中的混沌产生机理.This paper proposes a new algorithm for computing two-dimensional （un）stable manifolds in time continuous systems. With this algorithm, one can not only get a picture of a manifold efficiently, but also has many information of its every point, which are very useful for investigating the global dynamics of a system geometrically, such as features of stability region, evolution of the system flow and so on. The algorithm is mainly by finding many well distributed trajectories by solving initial value problems. An example on Lorenz system suggests this algorithm is very convenient. In addition, we study the chaotic dynamic of a three-dimensional neural network by detecting a heteroclinic orbit.

关 键 词：稳定流形 不稳定流形 动力系统 LORENZ系统 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]