Dynamical Systems (An Introduction to Complex Systems in Environment)
Mezemate Yacine, Schertzer Daniel
When we describe the evolution of a system we use several variables, i.e. a set of magnitudes, functions of space and time, the values of which define everything we know about the system completely and unambiguously. Then, the evolution of the systems is given by the evolution of the set of variables, according to some specific laws. A dynamic system is defined by a set of variables and a set of differential equations. During this lesson, we will focus on a mathematical description of dynamical systems using ODEs, we will discuss the stability in time of such systems and their evolution to the chaos. Third module of the course set "An Introduction to Complex Systems in Environment"Description
Université productrice
École nationale des ponts et chaussées, Université numérique ingénierie et technologie
Discipline
Ingénierie de l'environnement - Traitements de problèmes d'environnement, Ingénierie de l'environnement - Problèmes d'environnement
Mots clés
complex systems in environment, environmental engineering, système complexe, dynamical systems, ingénierie de l’environnement, non-linear dynamical system, chaos, Saddle-Node Bifurcation, Pitchfork Bifurcation, Hopf Bifurcation
Langues
Français
Droits attachés à la ressource
Licence CeCILL version 2
Indication pédagogique
Niveaux
L3
Type(s) pédagogique(s)
Cours / Présentation, Exercice
Type(s) documentaire(s)
Texte, Ressource interactive