Improved linear response for stochastically driven systems

Rafail Abramov
University of Chicago
Department of Mathematics

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction. However, in the case of stochastically driven dynamics one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics. Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that it is generally superior to the classical formula for both the additive and multiplicative stochastic forcing. This talk is based on the following paper: R. Abramov, "Improved linear response for stochastically driven systems", submitted to Journal of Nonlinear Science.

Presentation (PDF File)

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