基于自适应因子轨道延拓法的不变流形计算

贾蒙; 樊养余; 李慧敏

doi:10.7498/aps.59.7686

摘要

提出自适应因子和轨道延拓相结合的二维流形计算方法,利用以平衡点为中心的椭圆对局域流形的近似,通过轨道的等距延拓和椭圆初始点的自适应调节,在精度要求下自适应的添加轨道,完成二维双曲不变流形的计算.此方法比"轨道弧长法"精度高,包含更多细节信息;同时要比"盒子细分法"更能反映流形的延拓趋势.

关键词:

Most work on manifold study focuses on two-dimensional manifolds and there have been proposed some good computing methods. However, the computation of two-dimensional manifold is still a hot research field. In this paper the two-dimensional manifold of hyperbolic equilibria for vector fields is computed by combining self-adaptive parameter with trajectories continuation, approximating the local manifold with an ellipse around the equilibria, extending the trajectory with equal distance, and adjusting the trajectory with self-adaptive parameter. This method is more accurate than the "trajectories and arc-length method", and better shows the trend of the manifolds than the "box covering method".

Keywords:

作者及机构信息

(1)西北工业大学电子信息学院,西安 710072; (2)西北工业大学电子信息学院,西安 710072;新乡学院机电学院,新乡 453000

基金项目: 国家自然科学基金 (批准号: 60872159)资助的课题.

Authors and contacts

(1)Department of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China; (2)Department of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China;Department of Electrical Engineering, Xinxiang College, Xinxiang 453000, China

参考文献

[1]	Liu Y Z, Chen L Q, Cheng G, Ge X S 2000 Advance Mechanics 30 351 (in Chinese ) [刘延柱、陈立群、成功、戈新生 2000 力学进展 30 351]
[2]	Krauskopf B, Osinga H M 1998 Comput. Phys. 146 406
[3]	Doedel, Auto E J 1981 Congr. Numer 30 265
[4]	Nils Berglund http: //www.math.ethz.ch/~berglund 2001
[5]	Krauskopf B, Osinga H M 1999 Chaos 9 768
[6]	Johnson M E, Jolly M S, Kevrekidis I G 1997 Numer Algorithms 14 125
[7]	Guckenheimer J, Vladimirsky A 2004 Appl. Dyn. Sys. 3 232
[8]	Dellnitz M, Hobmann A 1997 Num. Math. 75 293
[9]	Krauskopf B, Osinga H M, Doedel E J 2005 Bifur. Chaos. Appl. Sci. Engrg 15 763
[10]	Krauskopf B, Osinga H M 2003 Appl. Dyn. Sys. 2 546
[11]	Guckenheimer J, Worfolk P 1993 Dynamical systems (Ithaca: Kluwer Academic) p241
[12]	Ni F, Xu W, Fang T, Yue X 2010 Chin. Phys. B 19 010510-1
[13]	Liu Y L, Zhu J, Luo X S 2009 Chin. Phys. B 18 3772
[14]	Jiang G R, Xu B G, Yang Q G 2009 Chin. Phys. B 18 5235
[15]	Hobson D 1993 Comput. Phys. 104 14
[16]	Henderson M E 2005 Appl. Dyn. Sys. 4 832
[17]	Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[18]	Zhang Y, Lei Y M, Fang T 2009 Acta Phys. Sin. 58 3799 (in Chinese)[张莹、雷佑铭、方同 2009物理学报 58 3799]
[19]	Jiang G R, Yang Q G 2008 Chin. Phys. B 17 4114
[20]	Zuo H L, Xu J X, Jiang J 2008 Chin. Phys. B 17 117
[21]	Xu Q, Tian Q 2009 Chin. Phys. B 18 2469

施引文献

[1]	Liu Y Z, Chen L Q, Cheng G, Ge X S 2000 Advance Mechanics 30 351 (in Chinese ) [刘延柱、陈立群、成功、戈新生 2000 力学进展 30 351]
[2]	Krauskopf B, Osinga H M 1998 Comput. Phys. 146 406
[3]	Doedel, Auto E J 1981 Congr. Numer 30 265
[4]	Nils Berglund http: //www.math.ethz.ch/~berglund 2001
[5]	Krauskopf B, Osinga H M 1999 Chaos 9 768
[6]	Johnson M E, Jolly M S, Kevrekidis I G 1997 Numer Algorithms 14 125
[7]	Guckenheimer J, Vladimirsky A 2004 Appl. Dyn. Sys. 3 232
[8]	Dellnitz M, Hobmann A 1997 Num. Math. 75 293
[9]	Krauskopf B, Osinga H M, Doedel E J 2005 Bifur. Chaos. Appl. Sci. Engrg 15 763
[10]	Krauskopf B, Osinga H M 2003 Appl. Dyn. Sys. 2 546
[11]	Guckenheimer J, Worfolk P 1993 Dynamical systems (Ithaca: Kluwer Academic) p241
[12]	Ni F, Xu W, Fang T, Yue X 2010 Chin. Phys. B 19 010510-1
[13]	Liu Y L, Zhu J, Luo X S 2009 Chin. Phys. B 18 3772
[14]	Jiang G R, Xu B G, Yang Q G 2009 Chin. Phys. B 18 5235
[15]	Hobson D 1993 Comput. Phys. 104 14
[16]	Henderson M E 2005 Appl. Dyn. Sys. 4 832
[17]	Liang C X, Tang J S 2008 Chin. Phys. B 17 135
[18]	Zhang Y, Lei Y M, Fang T 2009 Acta Phys. Sin. 58 3799 (in Chinese)[张莹、雷佑铭、方同 2009物理学报 58 3799]
[19]	Jiang G R, Yang Q G 2008 Chin. Phys. B 17 4114
[20]	Zuo H L, Xu J X, Jiang J 2008 Chin. Phys. B 17 117
[21]	Xu Q, Tian Q 2009 Chin. Phys. B 18 2469

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