Menu
Contact | A-Z
img

Project A3: Stochastic dynamics and bifurcations



Summary:

This project addresses central questions about nonlinear stochastic dynamics described by stochastic differential equations. The focus lies on noise-induced phenomena in systems undergoing bifurcations. Earlier studies of randomly perturbed slow--fast systems will be continued with detailed sample-path analysis of higher-dimensional bifurcations and an extension to partial differential equations. <br /> <br /> Going beyond local analysis, problems concerning global dynamics will be investigated. On the one hand, we will study random return maps with the goal of quantifying the effect of noise on global dynamics by a combination of precise local analysis near bifurcation points of the deterministic system and estimates on random return maps. On the other hand, two types of networks of randomly perturbed dynamical systems will be investigated: Networks of identical multistable systems with nearest-neighbour coupling, and small feed-forward networks with more complex local dynamics. In both cases the ultimate goal is the quantification of the combined effect of periodic forcing and random perturbations.


Links:

Random Dynamical Systems and Stochastic Processes in the Sciences

Recent Preprints:

13079 Nils Berglund, Barbara Gentz, Christian Kuehn PDF

From random Poincaré maps to stochastic mixed-mode-oscillation patterns

Project: A3, A9

Published: J. Dynam. Differential Equations 27, no. 1 (2015), 83–136

X

From random Poincaré maps to stochastic mixed-mode-oscillation patterns


Authors: Nils Berglund, Barbara Gentz, Christian Kuehn Projects: A3, A9
Submission Date: 2013-12-29 Submitter: Wolf-Jürgen Beyn
Download: PDF Link: 13079
Published: J. Dynam. Differential Equations 27, no. 1 (2015), 83–136

13024 Pierre Del Moral, Julian Tugaut PDF

Uniform propagation of chaos for a class of inhomogeneous diffusions

Project: A3

X

Uniform propagation of chaos for a class of inhomogeneous diffusions


Authors: Pierre Del Moral, Julian Tugaut Projects: A3
Submission Date: 2013-03-11 Submitter: Barbara Gentz
Download: PDF Link: 13024

12074 Nils Berglund, Barbara Gentz PDF

On the noise-induced passage through an unstable periodic orbit II: General case

Project: A3

Published: SIAM J. Math. Anal. 46, no. 1 (2014), 310-352

Notes: http://dx.doi.org/10.1137/120887965

X

On the noise-induced passage through an unstable periodic orbit II: General case


Authors: Nils Berglund, Barbara Gentz Projects: A3
Submission Date: 2012-08-16 Submitter: Michael Röckner
Download: PDF Link: 12074
Published: SIAM J. Math. Anal. 46, no. 1 (2014), 310-352
Notes: http://dx.doi.org/10.1137/120887965

12047 Friedrich Götze, Andrei Zaitsev PDF

Estimates for the rate of strong approximation in Hilbert space

Project: A3

X

Estimates for the rate of strong approximation in Hilbert space


Authors: Friedrich Götze, Andrei Zaitsev Projects: A3
Submission Date: 2012-06-11 Submitter: Michael Röckner
Download: PDF Link: 12047

12008 Nils Berglund, Barbara Gentz PDF

Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers’ law and beyond

Project: A3

Published: Electron. J. Probab. 18, no. 24 (2013), 1-58

X

Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers’ law and beyond


Authors: Nils Berglund, Barbara Gentz Projects: A3
Submission Date: 2012-02-10 Submitter: Moritz Kaßmann
Download: PDF Link: 12008
Published: Electron. J. Probab. 18, no. 24 (2013), 1-58

11092 Julian Tugaut PDF

Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Invariant probabilities

Project: A3

To appear: Journal of Theoretical Probability, July 2012 (2012)

X

Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Invariant probabilities


Authors: Julian Tugaut Projects: A3
Submission Date: 2011-10-04 Submitter: Barbara Gentz
Download: PDF Link: 11092
To appear: Journal of Theoretical Probability, July 2012 (2012)

11091 Julian Tugaut PDF

Exit problem of McKean-Vlasov diffusions in convex landscape

Project: A3

Published: Electronic Journal of Probability 17, no. Sept 12/ (2012), 1-26

X

Exit problem of McKean-Vlasov diffusions in convex landscape


Authors: Julian Tugaut Projects: A3
Submission Date: 2011-10-04 Submitter: Barbara Gentz
Download: PDF Link: 11091
Published: Electronic Journal of Probability 17, no. Sept 12/ (2012), 1-26

11090 Julian Tugaut PDF

Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Convergence

Project: A3

Published: Stochastic Processes and their applications (2013)

Notes: doi: http://dx.doi.org/10.1016/j.spa.2012.12.003

X

Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Convergence


Authors: Julian Tugaut Projects: A3
Submission Date: 2011-10-04 Submitter: Barbara Gentz
Download: PDF Link: 11090
Published: Stochastic Processes and their applications (2013)
Notes: doi: http://dx.doi.org/10.1016/j.spa.2012.12.003

11065 Julian Tugaut PDF

McKean-Vlasov diffusions: from the asynchronization to the synchronization

Project: A3

Published: C. R. Math. Acad. Sci. Paris 349, no. 17-18 (2011), 983–986

X

McKean-Vlasov diffusions: from the asynchronization to the synchronization


Authors: Julian Tugaut Projects: A3
Submission Date: 2011-07-26 Submitter: Barbara Gentz
Download: PDF Link: 11065
Published: C. R. Math. Acad. Sci. Paris 349, no. 17-18 (2011), 983–986

11063 Irina Kurkova, Kilian Raschel PDF

On the functions counting walks with small steps in the quarter plane

Project: A3

Published: Publications Mathématiques de l'IHÉS 116 (2012), 69-114

X

On the functions counting walks with small steps in the quarter plane


Authors: Irina Kurkova, Kilian Raschel Projects: A3
Submission Date: 2011-07-13 Submitter: Barbara Gentz
Download: PDF Link: 11063
Published: Publications Mathématiques de l'IHÉS 116 (2012), 69-114



Back
© 2017–2018 Sonderforschungbereich 701 | Privacy Policy