The Universal Plateau Structure of Lyapunov Exponents for Period Doubling Cascade Attractors |
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Authors: | WANG BingHong LI XiaoHu SUN Yong CHEN LongKang |
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Institution: | 1. Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
2. Department of Physics, Shenzhen University, Shenzhen 518060, China |
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Abstract: | Using algebraic. analysis method for periodic orbits of Hknon map, we derive the boundary equations of stable window and Lyapunov exponent plateau region on the space of nonintegrability parameter A and dissipation parameter J. Ekom the real root of these equations, we obtain the plateau width of Lyapunov exponent Wp = Ap,max - Ap,min and the stable tvindorv width Ws = Ap,max - Ap,min for high periodic orbits. The calculated result of plateau structure ratio α4 = Wp/WS for period-4 orbit agrees with the conjectural analytical formula: α4 = 2J2/(1+J4). Hence our result presents further evidence of universal dependence of Lyapunov exponent plateau structure on the dissipation parameter for period doubling cascade attractors of nonlinear system in transition from order to chaos. |
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Keywords: | Lyapunov exponent plateau period doubling cascade Hknon map transition between dissipative system and conservative system |
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