Stabilité des systèmes dynamiques avec applications
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Abstract
The objective of this dissertation is to study dynamical systems, both linear and nonlinear, using methods of mathematical and numerical analysis that describe the behavior of these systems around their equilibrium points and establish the necessary conditions to observe a specific phenomenon. The ultimate goal is to make qualitative and quantitative predictions about the behavior of a population based on parameters that describe its state. This study aims to understand and forecast the dynamics of a population in different contexts, using mathematical tools to analyze and interpret the obtained results.
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Keywords
Équations différentielles, Stabilité locale, Fonction de Lyapounov, Asymptotiquement stable, Modèles mathématiques, Proie-prédateur, Le Paradoxe de l'enrichissement, Differential equations, Local stability, Lyapounov function, Asymptotically stable, Mathematical models, Prey-Predator, The Paradox of enrichement.