基于径向增长因子的二维不变流形计算  

Computation of Two-dimensional Invariant Manifolds with Radial Growth Factor

作　　者：孙恒义[1] 樊养余[1] 李慧敏[1] 张菁[1] 贾蒙[1] 

机构地区：[1]西北工业大学电子信息学院,陕西西安710129

出　　处：《计算物理》2011年第4期621-625,共5页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(项目号:60872159)资助项目

摘　　要：在计算二维不变流形时,为均衡各方向的增长速度,便于构建动力系统的全局流形结构,引入径向控制因子对原始动力学系统进行归一化.以流的切向量的径向分量为标准,控制其在径向的增长速度.理论分析和实例计算的结果均表明,归一化后的动力学系统和原始系统的流同轨,即全局流形结构一致.最后,通过对Lorenz和Duffing系统的流形计算,表明该方法不仅能够达到测地线方法的控制效果,而且能够以离散流的形式进行计算,避免一系列复杂的边值问题.In order to balance growth rate of manifold in all directions and construct global manifold structure of a dynamical system,a radial control factor is adopted to normalize the original dynamical system.Taking radius component of the tangent vector as a standard,this method controls manifold expanding at same speed in all directions.Theoretical analysis and example calculation demonstrate that manifolds before and after normalization have same orbit with the original one,which means their global manifold structures are consistent.Lorenz and Duffing systems are taken for examples to demonstrate effectiveness of the proposed approach.It indicates that the method not only get same effect as geodesic process but also present manifold in discrete flow way,which avoids many complicated boundary value problems.

关 键 词：不变流形 流形计算 径向增长 洛伦兹系统 达芬系统 

分 类 号：O59[理学—应用物理]