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La théorie de la viabilité au service de la modélisation mathématique du développement durable. Application au cas de la forêt humide de Madagascar

Abstract : Sustainable development, initially defined as a mode of development that meets present needs without compromising the ability of future generations to meet their own needs, now suffers from the limitations of this definition. Since then, there are hundreds of definitions making the concept so vague that the most diverse political and economic measures claim to be sustainable. The aim of this thesis is to develop a model for sustainable development using the mathematical tools of the viability theory and to make this definition operational. The viability theory enables to integrate the main features of sustainable development : the multi-objective approach, the infinite time horizon, the possibility of determining several viable policies and actions and the respect of generational equity. The principle of viability is the study of dynamical controlled systems subjected to a constraint set. The main concept is the viability kernel, which is the set of all the initial states from which there is an evolution that remain in the constraint set. After underlying the limits of methods used in the modeling of sustainable development such as multi-criteria analysis, our scientific approach is based on the development of two mathematical models applied to the sustainable management of the forest corridor of Fianarantsoa (Madagascar). The challenge is to determine policy actions that meet two objectives : the conservation of the forest and the satisfaction of the needs of local people. Then, we demonstrate the usefulness of the theory of viability to achieve these objectives by defining the appropriate constraints and calculating the viability kernels.
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Claire Bernard. La théorie de la viabilité au service de la modélisation mathématique du développement durable. Application au cas de la forêt humide de Madagascar. Mathématiques générales [math.GM]. Université Blaise Pascal - Clermont-Ferrand II, 2011. Français. ⟨NNT : 2011CLF22158⟩. ⟨tel-00678594⟩

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