Detecting random bifurcations via rigorous enclosures of large deviations rate functions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912254165778432 |
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| author | Blessing, Alexandra Blumenthal, Alex Breden, Maxime Engel, Maximilian |
| author_facet | Blessing, Alexandra Blumenthal, Alex Breden, Maxime Engel, Maximilian |
| contents | 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-Fenichel 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detecting random bifurcations via rigorous enclosures of large deviations rate functions Blessing, Alexandra Blumenthal, Alex Breden, Maxime Engel, Maximilian Dynamical Systems Probability 37H15, 37H20, 60F10, 68V99 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-Fenichel 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. |
| title | Detecting random bifurcations via rigorous enclosures of large deviations rate functions |
| topic | Dynamical Systems Probability 37H15, 37H20, 60F10, 68V99 |
| url | https://arxiv.org/abs/2408.12556 |