基于广义Foliation条件的非线性映射二维流形计算

李慧敏; 樊养余; 孙恒义; 张菁; 贾蒙

西北工业大学电子信息学院,西安,710072

Growing two-dimensional manifold of nonlinear maps based on generalized Foliation condition

摘要: 主要研究非线性映射函数双曲不动点的二维流形计算问题.提出了推广的Foliation条件,以此来衡量二维流形上的一维流形轨道的增长量,进而控制各子流形的增长速度,实现二维流形在各个方向上的均匀增长.此外,提出了一种一维子流形轨道的递归插入算法,该算法巧妙地解决了二维流形面上网格点的插入、前像搜索,以及网格点后续轨道计算问题,同时插入的轨道不必从初始圆开始计算,避免了在初始圆附近产生过多的网格点.以超混沌三维Hénon映射和具有蝶形吸引子的Lorenz系统为例验证了算法的有效性.

关键词:

Abstract: In this paper we present an algorithm of computing two-dimensional（2D） stable and unstable manifolds of hyperbolic fixed points of nonlinear maps.The 2D manifold is computed by covering it with orbits of one-dimensional（1D） sub-manifolds.A generalized Foliation condition is proposed to measure the growth of 1D sub-manifolds and eventually control the growth of the 2D manifold along the orbits of 1D sub-manifolds in different directions.At the same time,a procedure for inserting 1D sub-manifolds between adjacent sub-manifolds is presented.The recursive procedure resolves the insertion of new mesh point,the searching for the image （or pre-image）,and the computation of the 1D sub-manifolds following the new mesh point tactfully,which does not require the 1D sub-manifolds to be computed from the initial circle and avoids the over assembling of mesh points.The performance of the algorithm is demonstrated with hyper chaotic three-dimensional（3D） Henon map and Lorenz system.

基于广义Foliation条件的非线性映射二维流形计算

西北工业大学电子信息学院,西安,710072

关键词:

Growing two-dimensional manifold of nonlinear maps based on generalized Foliation condition

西北工业大学电子信息学院,西安,710072

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