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:
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