基于插值与点映射相结合的全局分析方法  

A Global Analysis Method Based on Interpolation and Point Mapping

作　　者：刘梦军[1] 沈允文[1] 董海军[1] 

机构地区：[1]西北工业大学,西安710072

出　　处：《应用力学学报》2004年第1期26-29,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目 (批准号 5 0 0 75 0 70 )

摘　　要：利用插值的基本思想并结合点映射 ,提出了一种插值与点映射相结合的全局分析。通过吸引子之间的比较 ,判断相胞的顶点是否在同一吸引子的吸引域之内 ,从而识别出边界胞与非边界胞 ,并重点对边界胞进行处理 ,进而确定出相胞内各个相点的初值特性。通过比较与分析 ,本算法可以克服插值胞映射所存在的不足 ,算法简单且容易在计算机上实现。文中分析了算法产生误差的原因 。A new method based on cell mapping and point mapping is proposed to determine the basins of attraction of a nonlinear system's solutions in different steady states. The attractors are compared with each other to detect whether they are the same or not. And then the boundary cells can be distinguished. By judging whether their surrounding points are in the basin of an identical attractor, the initial characters of phase points will be determined for two kinds of cells respectively. The shortcomings in interpolated cell mapping method are overcome in this method. The sources of errors are analyzed. The algorithm is simple and can be easily performed on the computer.

关 键 词：插值 点映射 胞映射 全局分析 非线性动力学 不稳定不变集 激变现象 

分 类 号：O322[理学—一般力学与力学基础]