计算物理 ›› 2005, Vol. 22 ›› Issue (6): 79-84.
• 研究论文 • 上一篇 下一篇
李清都1, 杨晓松2
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LI Qing-du1, YANG Xiao-song2
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摘要： 提出了动力系统中稳定流形和不稳定流形的一种实用的快速算法,可以求得稳定流形和不稳定流形的直观图像,从而从几何角度研究动力系统的动态行为和稳定性区域的边界特征.算法由两步构成:①在不稳定流形上求得一些分布均匀的点,以精确反映流形的每个细节;②借助三角形剖分或二维单纯形剖分利用①的算法将这些点画出直观流形图像.
关键词: 稳定流形, 不稳定流形, Lorenz吸引子, 动力系统
Abstract: A practical and efficient computation method for stable and unstable manifolds is proposed.Pictures of unstable (stable) manifolds are obtained easily.Thus one can investigate geometrically dynamics of a dynamical system and features of stability regions.The algorithm consists of two steps:Firstly,calculate on well distributed points in the unstable manifold by means of integration so that details of the unstable manifold are shown.Secondly,draw a picture of the manifold with these points by means of triangle partition.
Key words: stable manifold, unstable manifold, Lorenz attractor, dynamic systems
中图分类号:
O193
李清都, 杨晓松. 二维不稳定流形的计算[J]. 计算物理, 2005, 22(6): 79-84.
LI Qing-du, YANG Xiao-song. Computation of Two Dimensional Unstable Manifolds[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 22(6): 79-84.
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http://www.cjcp.org.cn/CN/Y2005/V22/I6/79
