Modélisation globale et Caractérisation Topologique de dynamiques environnementales: de l'analyse des enveloppes fluides et du couvert de surface de la Terre à la caractérisation topolodynamique du chaos

Abstract : Theory of chaos deals with deterministic behaviors that are unpredictable at long term. This theory modifies fundamentally our concept of determinism, and shows the need to develope new analysis and modeling approaches in order to account for this essential property. One of these approaches is the global modeling technique which aim is to obtain models directly from experimental data. One important objective of the present work is to introduce new tools devoted to this technique initiated in the 1990s and to show its potential for the study of environmental dynamics. After presenting several analyses of environmental dynamics based on more classical approaches, the important concepts of chaos theory are presented and the global modeling technique is introduced. Such technique can be validated only based on well identified dynamics. The robustness of the global modeling technique is then tested on various cases presenting an increasing level of difficulty, starting from the Rössler chaotic system which variables exhibit different levels of observability, then considering cases of associated and aggregated dynamics, and then performing a multiple variables analysis. The global modeling technique is then applied to analyze environmental behaviors based on observational data. Applied to the cycles of cereal crops observed from space in semi-arid regions, a global model is obtained. This model is chaotic, weakly dissipative, and exhibits the first case of toroidal structure obtained from real data. This result is then confirmed by obtaining several models presenting these properties. The potential of the global modeling technique is also successfully tested on other environmental domains in hydrology and in eco-epidemiology. During the last two decades, topology of chaos has proven to be a powerful tool to characterize dynamical behaviors in a non ambiguous fashion. Nonetheless, its application field remains restricted since it could be applied only to strongly dissipative 3-dimensional systems. Obtaining weakly dissipative models brought us to cope with this hard problem and to introduce a new approach to deal with it. Applied to the first weakly dissipative chaotic system introduced by Lorenz in 1984 and to the cereal crops model obtained here with the global modeling technique, the first analyses of weakly dissipative chaotic dynamics could be performed, revealing behaviors of locally bidirectional extension of the flow. This new approach was then generalized in order to test its ability in higher dimension. It was possible to obtain the skeletons of 4D-suspensions for the Hénon (1976) and the super-Hénon chaotic maps, and also for the 3D-walking-stick hyperchaotic map introduced by Rössler in 1979. These overall work and results show the strong potential of the global modeling technique and the topological approach to analyze in a very consistent manner environmental behaviors observed from space by remote sensing, and more generally any chaotic dynamics.
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https://hal.ird.fr/tel-01100130
Contributor : Sylvain Mangiarotti <>
Submitted on : Tuesday, January 6, 2015 - 12:47:22 AM
Last modification on : Friday, October 11, 2019 - 8:22:26 PM
Long-term archiving on : Tuesday, April 7, 2015 - 10:46:23 AM

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  • HAL Id : tel-01100130, version 1

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S. Mangiarotti. Modélisation globale et Caractérisation Topologique de dynamiques environnementales: de l'analyse des enveloppes fluides et du couvert de surface de la Terre à la caractérisation topolodynamique du chaos. Sciences du Vivant [q-bio]. Université de Toulouse 3, 2014. ⟨tel-01100130⟩

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