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Linear response theory for statistical ensembles in complex systems with time-periodic forcing. (English) Zbl 1201.37109
The authors considered some dynamical systems governed by stochastic differential equations where the coefficients are periodic. Periodicity is a natural assumption due to the seasonal cycle and the climate change studies. The aim is to provide some response formula when the forcing term is time periodic. These response formulas are developed through the mathematical interplay between statistical solutions of the time periodic dynamical systems and the related skew-product system. Some simulations are given when there is zero noise. The effect of the noise is also studied.

MSC:
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
86A99 Geophysics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34C28 Complex behavior and chaotic systems of ordinary differential equations
94A15 Information theory (general)
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