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Symbolic dynamics of the Lorenz equations
Fang, HP; Hao, BL; Fang, HP , ACAD SINICA,INST THEORET PHYS,POB 2735,BEIJING 100080,PEOPLES R CHINA.
1996
发表期刊CHAOS SOLITONS & FRACTALS
ISSN0960-0779
卷号7期号:2页码:217-246
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.
部门归属INT CTR THEORET PHYS,I-34100 TRIESTE,ITALY; FUDAN UNIV,DEPT PHYS,SHANGHAI 200433,PEOPLES R CHINA
关键词Henon Map Strange Attractor Chaos Convection
学科领域Physics
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收录类别SCI
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/12655
专题理论物理所1978-2010年知识产出
通讯作者Fang, HP , ACAD SINICA,INST THEORET PHYS,POB 2735,BEIJING 100080,PEOPLES R CHINA.
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Fang, HP,Hao, BL,Fang, HP , ACAD SINICA,INST THEORET PHYS,POB 2735,BEIJING 100080,PEOPLES R CHINA.. Symbolic dynamics of the Lorenz equations[J]. CHAOS SOLITONS & FRACTALS,1996,7(2):217-246.
APA Fang, HP,Hao, BL,&Fang, HP , ACAD SINICA,INST THEORET PHYS,POB 2735,BEIJING 100080,PEOPLES R CHINA..(1996).Symbolic dynamics of the Lorenz equations.CHAOS SOLITONS & FRACTALS,7(2),217-246.
MLA Fang, HP,et al."Symbolic dynamics of the Lorenz equations".CHAOS SOLITONS & FRACTALS 7.2(1996):217-246.
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