Analytical approximations of Lotka-Volterra integrals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914792489353216 |
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| author | Lundström, Niklas L. P. Söderbacka, Gunnar J. |
| author_facet | Lundström, Niklas L. P. Söderbacka, Gunnar J. |
| contents | In this note we derive simple analytical bounds for solutions of $x - \ln x = y -\ln y$ and use them for estimating trajectories following Lotka-Volterra-type integrals. We show how our results imply estimates for the Lambert $W$ function as well as for trajectories of general predator-prey systems, including e.g. Rosenzweig-MacArthur equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analytical approximations of Lotka-Volterra integrals Lundström, Niklas L. P. Söderbacka, Gunnar J. Dynamical Systems In this note we derive simple analytical bounds for solutions of $x - \ln x = y -\ln y$ and use them for estimating trajectories following Lotka-Volterra-type integrals. We show how our results imply estimates for the Lambert $W$ function as well as for trajectories of general predator-prey systems, including e.g. Rosenzweig-MacArthur equations. |
| title | Analytical approximations of Lotka-Volterra integrals |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2311.03069 |