Unifying Lyapunov exponents with probabilistic uncertainty quantification
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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_ | 1866910364697886720 |
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| author | Blake, Liam Maclean, John Balasuriya, Sanjeeva |
| author_facet | Blake, Liam Maclean, John Balasuriya, Sanjeeva |
| contents | The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with stochastic sensitivity (which quantifies the uncertainty of an evolving uncertain system whose initial condition is certain) within a finite time uncertainty quantification framework in which both the dynamics and the initial condition of a continuously evolving $ n $-dimensional state variable are uncertain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unifying Lyapunov exponents with probabilistic uncertainty quantification Blake, Liam Maclean, John Balasuriya, Sanjeeva Dynamical Systems Chaotic Dynamics Data Analysis, Statistics and Probability The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with stochastic sensitivity (which quantifies the uncertainty of an evolving uncertain system whose initial condition is certain) within a finite time uncertainty quantification framework in which both the dynamics and the initial condition of a continuously evolving $ n $-dimensional state variable are uncertain. |
| title | Unifying Lyapunov exponents with probabilistic uncertainty quantification |
| topic | Dynamical Systems Chaotic Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2403.05085 |