中国物理B ›› 1994, Vol. 3 ›› Issue (9): 653-666.doi: 10.1088/1004-423X/3/9/002

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THE UNIVERSAL TRANSITION OF PLATEAU STRUCTURE OF LYAPUNOV EXPONENTS

汪秉宏1, 陈国义2, 顾国庆3   

  1. (1)Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China;Department of System Science and System Engineering, Shanghai Institute of Mechanical Engineering, Shanghai 200093, China; (2)Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China; (3)Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China;Department of System Science and System Engineering, Shanghai Institute of Mechanical Engineering, Shanghai 200093, China
  • 收稿日期:1993-07-26 出版日期:1994-09-20 发布日期:1994-09-20
  • 基金资助:
    Project supported by the National Basic Research Project "Nonlinear Science".

THE UNIVERSAL TRANSITION OF PLATEAU STRUCTURE OF LYAPUNOV EXPONENTS

WANG BING-HONG (汪秉宏)abc, CHEN GUO-YI (陈国义)b, GU GUO-QING (顾国庆)bc   

  1. a Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; b Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China; c Department of System Science and System Engineering, Shanghai Institute of Mechanical Engineering, Shanghai 200093, China
  • Received:1993-07-26 Online:1994-09-20 Published:1994-09-20
  • Supported by:
    Project supported by the National Basic Research Project "Nonlinear Science".

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摘要： The universal transition of Lyapunov exponents between conservative limit and dissipa-tire limit of nonlinear dynamical system is studied. It is discovered numerically and proved analytically that for homogeneous dissipative two-dimensional maps, along the equal dissi-pation line in parameter space, the Lyapunov exponents of attractor orbits possess a plateau structure and strict symmetry about its plateau value, The ratios between the plateau width and the stable window width of period 1-4 orbits for Henon map are calculated. The result shows that the plateau structure of Lyapunov exponents remains invariant for the attractor orbits belonging to a period doubling bifurcation sequence. This fact reveals a new universal transition behavior between order and chaos when the dissipation of the dynamical system is weakened to zero.

Abstract: The universal transition of Lyapunov exponents between conservative limit and dissipa-tire limit of nonlinear dynamical system is studied. It is discovered numerically and proved analytically that for homogeneous dissipative two-dimensional maps, along the equal dissi-pation line in parameter space, the Lyapunov exponents of attractor orbits possess a plateau structure and strict symmetry about its plateau value, The ratios between the plateau width and the stable window width of period 1-4 orbits for Henon map are calculated. The result shows that the plateau structure of Lyapunov exponents remains invariant for the attractor orbits belonging to a period doubling bifurcation sequence. This fact reveals a new universal transition behavior between order and chaos when the dissipation of the dynamical system is weakened to zero.

中图分类号:  (Numerical simulations of chaotic systems)

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02.30.Oz (Bifurcation theory) 02.30.Uu (Integral transforms)