Quadratic response of random and deterministic dynamical systems

We consider the linear and quadratic higher-order terms associated with the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the stationary measure with respect to the changes in the system its...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2020-02, Vol.30 (2), p.023113-023113
Main Authors: Galatolo, Stefano, Sedro, Julien
Format: Article
Language:English
Subjects:
Dynamical Systems
Mathematics
Perturbation
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Summary:We consider the linear and quadratic higher-order terms associated with the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the stationary measure with respect to the changes in the system itself, expressing how the statistical properties of the system vary under the perturbation. We show a general framework in which one can obtain rigorous convergence and formulas for these two terms. The framework is flexible enough to be applied both to deterministic and random systems. We give examples of such an application computing linear and quadratic response for Arnold maps with additive noise and deterministic expanding maps.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.5122658