Coupling Sensitivity of Chaos
Open Access
- 1 January 1984
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics Supplement
- Vol. 79, 75-95
- https://doi.org/10.1143/ptps.79.75
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 and likewise for L(i)(d)−L as well where L(1)(0) = L(1)(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.Keywords
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