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Acta Physica Sinica (Overseas Edition), 1994, Vol. 3(9): 653-666    DOI: 10.1088/1004-423X/3/9/002
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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
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
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.
Received:  26 July 1993      Accepted manuscript online: 
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  02.30.Oz (Bifurcation theory)  
  02.30.Uu (Integral transforms)  
Fund: Project supported by the National Basic Research Project "Nonlinear Science".

Cite this article: 

WANG BING-HONG (汪秉宏), CHEN GUO-YI (陈国义), GU GUO-QING (顾国庆) THE UNIVERSAL TRANSITION OF PLATEAU STRUCTURE OF LYAPUNOV EXPONENTS 1994 Acta Physica Sinica (Overseas Edition) 3 653

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