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题名: Symbolic dynamics of the Lorenz equations
作者: Fang, HP ;  Hao, BL
刊名: CHAOS SOLITONS & FRACTALS
出版日期: 1996
卷号: 7, 期号:2, 页码:217-246
关键词: HENON MAP ;  STRANGE ATTRACTOR ;  CHAOS ;  CONVECTION
学科分类: Physics
通讯作者: Fang, HP , ACAD SINICA,INST THEORET PHYS,POB 2735,BEIJING 100080,PEOPLES R CHINA.
部门归属: INT CTR THEORET PHYS,I-34100 TRIESTE,ITALY; FUDAN UNIV,DEPT PHYS,SHANGHAI 200433,PEOPLES R CHINA
英文摘要: The Lorenz equations are investigated in a wide range of parameters by using the method of symbolic dynamics. First, the systematics of stable periodic orbits in the Lorenz equations is compared with that of the one-dimensional (1D) cubic map, which shares the same discrete symmetry with the Lorenz model. It encompasses all the known periodic windows of the Lorenz equations with only one exception. Second, in order to justify the above approach and to understand the exceptions, another 1D map with a discontinuity is extracted from an extension of the geometric Lorenz attractor and its symbolic dynamics is constructed. All this has to be done in the light of symbolic dynamics of two-dimensional maps. Finally, symbolic dynamics for the actual Poincare return map of the Lorenz equations is constructed in a heuristic way. New periodic windows of the Lorenz equations and their parameters can be predicted from this symbolic dynamics in combination with the 1D cubic map. The extended geometric 2D Lorenz map and the 1D antisymmetric map with a discontinuity describe the topological aspects of the Lorenz equations to high accuracy.
收录类别: SCI
原文出处: 查看原文
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/12655
Appears in Collections:理论物理所1978-2010年知识产出_期刊论文

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Recommended Citation:
Fang, HP,Hao, BL. Symbolic dynamics of the Lorenz equations[J]. CHAOS SOLITONS & FRACTALS,1996,7(2):217-246.
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