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Nonlin. Processes Geophys., 14, 681-694, 2007
https://doi.org/10.5194/npg-14-681-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
 
31 Oct 2007
Fluctuation-Response Relation and modeling in systems with fast and slow dynamics
G. Lacorata1 and A. Vulpiani2 1Institute of Atmospheric and Climate Sciences, National Research Council, Str. Monteroni, 73100 Lecce, Italy
2Department of Physics and INFN, University of Rome "La Sapienza", P.le A. Moro 2, 00185 Roma, Italy
Abstract. We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables. The method is tested by using the 360-variable Lorenz-96 model, where slow and fast variables are coupled to one another with reciprocal feedback, and a simplified low dimensional system. In the Fluctuation-Response context, the influence of the fast dynamics on the slow dynamics relies in a non trivial behavior of a suitable quadratic response function. This has important consequences for the modeling of the slow dynamics in terms of a Langevin equation: beyond a certain intrinsic time interval even the optimal model can give just statistical prediction.

Citation: Lacorata, G. and Vulpiani, A.: Fluctuation-Response Relation and modeling in systems with fast and slow dynamics, Nonlin. Processes Geophys., 14, 681-694, https://doi.org/10.5194/npg-14-681-2007, 2007.
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