Journal
CHINESE ANNALS OF MATHEMATICS SERIES B
Volume 30, Issue 5, Pages 447-462Publisher
SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
DOI: 10.1007/s11401-009-0088-3
Keywords
Fluctuation-dissipation theorem; Linear response
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Funding
- National Science Foundation [DMS-0608984]
- Office of Naval Research [N00014-06-1-0286]
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The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the short-time linear response formula with the full rank tangent map can be expensive. Here, a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed. The conditions for which the short, time linear response approximation with the reduced-rank tangent map is valid are established, and two practical situations are examined, where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.
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