A random dynamical systems perspective on stochastic resonance

Cherubini, Anna Maria; Lamb, Jeroen S. W.; Rasmussen, Martin; Sato, Yuzuru

doi:10.1088/1361-6544/aa72bd

Cited by 28 publications

(28 citation statements)

References 33 publications

(38 reference statements)

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“…The bifurcation sequence, when increasing the control parameter (a surrogate of the Reynolds number), evolves from a high-dimensional noisy fixed point to a lower dimensional structure where the dynamics of the jet switches between blocked and zonal flows. Possible explanations of these phenomena of noise-induced order are investigated in the framework of stochastic dynamical systems 32 , 33 .…”

Section: Discussionmentioning

confidence: 99%

The hammam effect or how a warm ocean enhances large scale atmospheric predictability

et al. 2019

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The atmosphere’s chaotic nature limits its short-term predictability. Furthermore, there is little knowledge on how the difficulty of forecasting weather may be affected by anthropogenic climate change. Here, we address this question by employing metrics issued from dynamical systems theory to describe the atmospheric circulation and infer the dynamical properties of the climate system. Specifically, we evaluate the changes in the sub-seasonal predictability of the large-scale atmospheric circulation over the North Atlantic for the historical period and under anthropogenic forcing, using centennial reanalyses and CMIP5 simulations. For the future period, most datasets point to an increase in the atmosphere’s predictability. AMIP simulations with 4K warmer oceans and 4 × atmospheric CO2 concentrations highlight the prominent role of a warmer ocean in driving this increase. We term this the hammam effect. Such effect is linked to enhanced zonal atmospheric patterns, which are more predictable than meridional configurations.

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Section: Discussionmentioning

confidence: 99%

The hammam effect or how a warm ocean enhances large scale atmospheric predictability

et al. 2019

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“…The following notion of almost periodicity appeared in [39], in the context of continuous random dynamical systems. It is the natural generalization of the notion of periodicity investigated by Zhao and his collaborators [18,19,20,21,40], see also Cherubini et al [14] for periodicity in the nonautonomous case. Similarly, the notion of stationarity below (in the autonomous case) can be found in [28].…”

Section: θ-Almost Periodicity and θ-Periodicitymentioning

confidence: 97%

Almost periodicity and periodicity for nonautonomous random dynamical systems

Fitte

2020

Stoch. Dyn.

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We present a notion of almost periodicity which can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept allows for improvements of known results of almost periodicity in distribution, for general random processes and for solutions to stochastic differential equations.

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“…Over the last decade significant progress has been made in the study of the long-time behaviour of SDE's generated by time-dependent vector fields (e.g. [20,[31][32][33]86,87,89]). Based on the insight from the latter results, we shall study the ergodicity of SDE's with time-periodic coefficients in order to establish fluctuationdissipation formulas through the linear response in the random periodic regime.…”

Section: General Set-upmentioning

confidence: 99%

Time-periodic measures, random periodic orbits, and the linear response for dissipative non-autonomous stochastic differential equations

Branicki

Uda

2021

Res Math Sci

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We consider a class of dissipative stochastic differential equations (SDE’s) with time-periodic coefficients in finite dimension, and the response of time-asymptotic probability measures induced by such SDE’s to sufficiently regular, small perturbations of the underlying dynamics. Understanding such a response provides a systematic way to study changes of statistical observables in response to perturbations, and it is often very useful for sensitivity analysis, uncertainty quantification, and improving probabilistic predictions of nonlinear dynamical systems, especially in high dimensions. Here, we are concerned with the linear response to small perturbations in the case when the time-asymptotic probability measures are time-periodic. First, we establish sufficient conditions for the existence of stable random time-periodic orbits generated by the underlying SDE. Ergodicity of time-periodic probability measures supported on these random periodic orbits is subsequently discussed. Then, we derive the so-called fluctuation–dissipation relations which allow to describe the linear response of statistical observables to small perturbations away from the time-periodic ergodic regime in a manner which only exploits the unperturbed dynamics. The results are formulated in an abstract setting, but they apply to problems ranging from aspects of climate modelling, to molecular dynamics, to the study of approximation capacity of neural networks and robustness of their estimates.

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A random dynamical systems perspective on stochastic resonance

Cited by 28 publications

References 33 publications

The hammam effect or how a warm ocean enhances large scale atmospheric predictability

The hammam effect or how a warm ocean enhances large scale atmospheric predictability

Almost periodicity and periodicity for nonautonomous random dynamical systems

Time-periodic measures, random periodic orbits, and the linear response for dissipative non-autonomous stochastic differential equations

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