A numerical framework to understand transitions in high-dimensional stochastic dynamical systems

Henk Dijkstra; Alexis Tantet; Jan Viebahn; Erik Mulder; Mariët  Hebbink; Daniele Castellana; Henri van den Pol; Jason Frank; Sven Baars; Friederik Wubs; Mikael Chekroun; Christian Kuehn

doi:10.1093/climsys/dzw003

A numerical framework to understand transitions in high-dimensional stochastic dynamical systems

Henk Dijkstra^*, Alexis Tantet, Jan Viebahn, Erik Mulder, Mariët Hebbink, Daniele Castellana, Henri van den Pol, Jason Frank, Sven Baars, Friederik Wubs, Mikael Chekroun, Christian Kuehn

^*Corresponding author for this work

Computational and Numerical Mathematics

Research output: Contribution to journal › Article › Academic › peer-review

354 Downloads (Pure)

Abstract

Dynamical systems methodology is a mature complementary approach to forward simulation which can be used to investigate many aspects of climate dynamics. With this paper, a review is given on the methods to analyse deterministic and stochastic climate models and show that these are not restricted to low-dimensional toy models, but that they can be applied to models formulated by stochastic partial differential equations. We sketch the numerical implementation of these methods and illustrate these by showing results for two canonical problems in climate dynamics.

Original language	English
Number of pages	9
Journal	Dynamics and Statistics of the Climate System: An Interdisciplinary Journal
Volume	1
Issue number	1
DOIs	https://doi.org/10.1093/climsys/dzw003
Publication status	Published - 30-Nov-2016

Access to Document

10.1093/climsys/dzw003Licence: CC BY-NC

A numerical framework to understand transitions in high-dimensional stochastic dynamical systemsFinal publisher's version, 4.74 MBLicence: CC BY-NC

Handle.net

Persistent link

Cite this

Dijkstra, H., Tantet, A., Viebahn, J., Mulder, E., Hebbink, M., Castellana, D., van den Pol, H., Frank, J., Baars, S., Wubs, F., Chekroun, M., & Kuehn, C. (2016). A numerical framework to understand transitions in high-dimensional stochastic dynamical systems. Dynamics and Statistics of the Climate System: An Interdisciplinary Journal, 1(1). https://doi.org/10.1093/climsys/dzw003

@article{f2efd03758554d7abe3f1d452e045e89,

title = "A numerical framework to understand transitions in high-dimensional stochastic dynamical systems",

abstract = "Dynamical systems methodology is a mature complementary approach to forward simulation which can be used to investigate many aspects of climate dynamics. With this paper, a review is given on the methods to analyse deterministic and stochastic climate models and show that these are not restricted to low-dimensional toy models, but that they can be applied to models formulated by stochastic partial differential equations. We sketch the numerical implementation of these methods and illustrate these by showing results for two canonical problems in climate dynamics.",

author = "Henk Dijkstra and Alexis Tantet and Jan Viebahn and Erik Mulder and Mari{\"e}t Hebbink and Daniele Castellana and {van den Pol}, Henri and Jason Frank and Sven Baars and Friederik Wubs and Mikael Chekroun and Christian Kuehn",

year = "2016",

month = nov,

day = "30",

doi = "10.1093/climsys/dzw003",

language = "English",

volume = "1",

journal = "Dynamics and Statistics of the Climate System: An Interdisciplinary Journal",

publisher = "Oxford University Press",

number = "1",

}

Dijkstra, H, Tantet, A, Viebahn, J, Mulder, E, Hebbink, M, Castellana, D, van den Pol, H, Frank, J, Baars, S, Wubs, F, Chekroun, M & Kuehn, C 2016, 'A numerical framework to understand transitions in high-dimensional stochastic dynamical systems', Dynamics and Statistics of the Climate System: An Interdisciplinary Journal, vol. 1, no. 1. https://doi.org/10.1093/climsys/dzw003

TY - JOUR

T1 - A numerical framework to understand transitions in high-dimensional stochastic dynamical systems

AU - Dijkstra, Henk

AU - Tantet, Alexis

AU - Viebahn, Jan

AU - Mulder, Erik

AU - Hebbink, Mariët

AU - Castellana, Daniele

AU - van den Pol, Henri

AU - Frank, Jason

AU - Baars, Sven

AU - Wubs, Friederik

AU - Chekroun, Mikael

AU - Kuehn, Christian

PY - 2016/11/30

Y1 - 2016/11/30

N2 - Dynamical systems methodology is a mature complementary approach to forward simulation which can be used to investigate many aspects of climate dynamics. With this paper, a review is given on the methods to analyse deterministic and stochastic climate models and show that these are not restricted to low-dimensional toy models, but that they can be applied to models formulated by stochastic partial differential equations. We sketch the numerical implementation of these methods and illustrate these by showing results for two canonical problems in climate dynamics.

AB - Dynamical systems methodology is a mature complementary approach to forward simulation which can be used to investigate many aspects of climate dynamics. With this paper, a review is given on the methods to analyse deterministic and stochastic climate models and show that these are not restricted to low-dimensional toy models, but that they can be applied to models formulated by stochastic partial differential equations. We sketch the numerical implementation of these methods and illustrate these by showing results for two canonical problems in climate dynamics.

U2 - 10.1093/climsys/dzw003

DO - 10.1093/climsys/dzw003

M3 - Article

VL - 1

JO - Dynamics and Statistics of the Climate System: An Interdisciplinary Journal

JF - Dynamics and Statistics of the Climate System: An Interdisciplinary Journal

IS - 1

ER -

A numerical framework to understand transitions in high-dimensional stochastic dynamical systems

Abstract

Access to Document

Handle.net

Fingerprint

Cite this