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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Sep;66(3 Pt 2A):036103. Epub 2002 Sep 6.

Linear response of the Lorenz system.

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Alfred-Wegener-Institute for Polar and Marine Research, Columbusstrasse, D-27568 Bremerhaven, Germany.


The present numerical study provides strong evidence that at standard parameters the response of the Lorenz system to small perturbations of the control parameter r is linear. This evidence is obtained not only directly by determining the response in the observable A(x)=z, but also indirectly by validating various implications of the assumption of a linear response, like a quadratic response at twice the perturbation frequency, a vanishing response in A(x)=x, the Kramers-Kronig relations, and relations between different response functions. Since the Lorenz system is nonhyperbolic, the present results indicate that in contrast to a recent speculation the large system limit (thermodynamic limit) need not be invoked to obtain a linear response for chaotic systems of this type.


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