Publikation: Detecting random bifurcations via rigorous enclosures of large deviations rate functions
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2025
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Physica D: Nonlinear Phenomena. Elsevier. 2025, 476, 134617. ISSN 0167-2789. eISSN 1872-8022. Verfügbar unter: doi: 10.1016/j.physd.2025.134617
Zusammenfassung
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of moment Lyapunov exponents which are principal eigenvalues of the generator of the tilted (Feynman–Kac) semigroup. Using a computer assisted proof, we demonstrate how to determine these eigenvalues and investigate the rate function which is the Legendre–Fenchel transform of the moment Lyapunov function. We apply our results to two case studies: the pitchfork bifurcation and a two-dimensional toy model, also considering the transition to a positive asymptotic Lyapunov exponent.
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Fachgebiet (DDC)
510 Mathematik
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Random bifurcations, Finite time Lyapunov exponents, Moment Lyapunov exponents, Large deviations
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BLESSING-NEAMTU, Alexandra, Alex BLUMENTHAL, Maxime BREDEN, Maximilian ENGEL, 2025. Detecting random bifurcations via rigorous enclosures of large deviations rate functions. In: Physica D: Nonlinear Phenomena. Elsevier. 2025, 476, 134617. ISSN 0167-2789. eISSN 1872-8022. Verfügbar unter: doi: 10.1016/j.physd.2025.134617BibTex
@article{BlessingNeamtu2025-06Detec-73768,
title={Detecting random bifurcations via rigorous enclosures of large deviations rate functions},
year={2025},
doi={10.1016/j.physd.2025.134617},
volume={476},
issn={0167-2789},
journal={Physica D: Nonlinear Phenomena},
author={Blessing-Neamtu, Alexandra and Blumenthal, Alex and Breden, Maxime and Engel, Maximilian},
note={Article Number: 134617}
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<dcterms:abstract>The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of moment Lyapunov exponents which are principal eigenvalues of the generator of the tilted (Feynman–Kac) semigroup. Using a computer assisted proof, we demonstrate how to determine these eigenvalues and investigate the rate function which is the Legendre–Fenchel transform of the moment Lyapunov function. We apply our results to two case studies: the pitchfork bifurcation and a two-dimensional toy model, also considering the transition to a positive asymptotic Lyapunov exponent.</dcterms:abstract>
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