Stochastic parameterisations and memory effects in Multilevel Systems
Abstract
We use Ruelle's response theory to study the impact of weakly coupling two dynamical systems on the statistics of long-term averaged observations of one of the subsystems. We analyze how the resulting perturbations can be written as depending only on the variables of the system of interest. At first order in the coupling strength the coupling has the same effect as a constant perturbation. At second order, there are two separate and very different contributions. One is a term taking into account the second order contributions of the fluctuations in the coupling. This can be parameterised by a stochastic noise term on the single system dynamics. The other term is a memory term, coupling the single system dynamics to itself, through correlations present in the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to deal with such a perturbation, we also present an extension to Ruelle's response theory for perturbation with memory.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2011
- Bibcode:
- 2011AGUFMNG33B1512L
- Keywords:
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- 3235 MATHEMATICAL GEOPHYSICS / Persistence;
- memory;
- correlations;
- clustering;
- 3265 MATHEMATICAL GEOPHYSICS / Stochastic processes;
- 4430 NONLINEAR GEOPHYSICS / Complex systems;
- 4445 NONLINEAR GEOPHYSICS / Nonlinear differential equations