Speaker
Description
Global modelling such as GPoM \cite{Mangiarotti2012} is a tool for constructing systems of polynomial differential equations from time series. We present one use of this tool for variable selection. We study the bloom of the toxic algae (\textit{Ostreopsis} cf. \textit{ovata}) \cite{FabriRuiz2024} and look for strong relationships between the alga and its environment (from COPERNICUS datasets) through the lens of dynamics. Using time series, we have highlighted other links that exist between the proliferation of this algae and salinity, oxygen, or nutrient concentrations.
The second part of the talk is dedicated to the chaotic dynamics emerging from the numerous ordinary differential equations systems generated with GPoM. The comparison of models is performed using topological characterization of the chaotic attractors \cite{rosalie2016template, Rosalie2025}. It enables to reduce the number candidates to a smaller set of systems that are able to reproduce dynamics observed in the data. Structures of the polynomial models of ordinary differential equations systems will be discussed as well.
Bibliography
@article{FabriRuiz2024,
title = {Harmful Ostreopsis cf. ovata blooms could extend in time span with climate change in the Western Mediterranean Sea},
volume = {947},
ISSN = {0048-9697},
url = {http://dx.doi.org/10.1016/j.scitotenv.2024.174726},
DOI = {10.1016/j.scitotenv.2024.174726},
journal = {Science of The Total Environment},
publisher = {Elsevier BV},
author = {Fabri-Ruiz, S. and Berdalet, E. and Ulses, C. and Somot, S. and Vila, M. and Lemée, R. and Irisson, J.-O.},
year = {2024},
month = oct,
pages = {174726}
}
@article{Mangiarotti2012,
title = {Polynomial search and global modeling: Two algorithms for modeling chaos},
author = {Mangiarotti, S. and Coudret, R. and Drapeau, L. and Jarlan, L.},
journal = {Phys. Rev. E},
volume = {86},
issue = {4},
pages = {046205},
numpages = {14},
year = {2012},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.86.046205},
url = {https://link.aps.org/doi/10.1103/PhysRevE.86.046205}
}
@article{rosalie2016template,
title = {Templates and subtemplates of Rössler attractors from a bifurcation diagram},
author = {Rosalie, M. },
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {49},
number = {31},
pages = {315101},
year = {2016},
doi = {10.1088/1751-8113/49/31/315101},
langid = {english}
}
@article{Rosalie2025,
title = {Structure analysis of the Lorenz-84 chaotic attractor},
volume = {35},
ISSN = {1089-7682},
url = {http://dx.doi.org/10.1063/5.0287725},
DOI = {10.1063/5.0287725},
number = {10},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
publisher = {AIP Publishing},
author = {Rosalie, M. and Mangiarotti, S.},
year = {2025},
month = {10}
}
