Coupling Sensitivity of Chaos : A New Universal Property of Chaotic Dynamical Systems
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概要
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It is shown that chaos exhibited by one-dimensional maps X_<n+1>=F(X_n) is strongly sensitive to couplings to another identical chaos as to the Lyapunov exponents. Namely, for two-dimensional maps such as X_<n+1>=F(X_n)+d・D(Y_n,X_n),Y_<n+1>=F(Y_n)+d・D(X_n,Y_n),the first and second Lyapunov exponents (L^<(i)>(d),i=1,2) behave for small d as L^<(1)>(d)-L^<(2)>(d)∝1/(-1nd) and likewise for L^<(i)>(d)-L as well where L^<(1)>(0)=L^<(2)>(0)=L>0. Numerical evidences for various F(X)'s and a variety of couplings are given. A perturbation theory as well as a renormalization group-like theory is developed to explain this new universal property of chaotic systems which we call coupling sensitivity of chaos. A generalization of this notion is also attempted which leads us to an interesting problem.
- 理論物理学刊行会の論文
- 1985-03-20
著者
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DAIDO Hiroaki
Department of Physics, Kyoto University
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Daido Hiroaki
Research Institute For Fundamental Physics Kyoto University : Fellow Of The Japan Society For The Pr
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Daido Hiroaki
Research Institute For Fundamental Physics Kyoto University
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DAIDO Hiroaki
Research Institute for Fundamental Physics, Kyoto University : Fellow of the Japan Society for the Promotion of Science : Present address:Institut fur Theoretische Physik, Universityersitat Stuttgart
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