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Prog. Theor. Phys. Supplement No.79 (1984) pp. 75-95

[ Full Text PDF : FREE ACCESS (1149K) ]

Coupling Sensitivity of Chaos

— A New Universal Property of Chaotic Dynamical Systems —

Hiroaki Daido

Research Institute for Fundamental Physics, Kyoto University, Kyoto 606

(Received March 24, 1984)

Abstract:

It is shown that chaos exhibited by one-dimensional maps Xn+1 = F(Xn) is strongly sensitive to couplings to another identical chaos as to the Lyapunov exponents. Namely, for two-dimensional maps such as Xn+1 = F(Xn) + d · D(Yn, Xn), Yn+1 = F(Yn) + d · D(Xn, Yn), the first and second Lyapunov exponents (L(i)(d) , i = 1, 2) behave for small d as
L(1)(d) - L(2)(d) ∝ 1/(- ln d)
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.


URL : http://ptp.ipap.jp/link?PTPS/79/75/
DOI : 10.1143/PTPS.79.75

[ Full Text PDF : FREE ACCESS (1149K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Supplement No.79 (1984) pp. 96-124 :
    Statistical Mechanics of Intermittent Chaos
    Yoji Aizawa, Chikara Murakami and Tamotsu Kohyama

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