Abstract
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 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 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.
- Received 2 October 2001
DOI:https://doi.org/10.1103/PhysRevE.66.036103
©2002 American Physical Society