URI http://ori.unit-c.fr/uid/unit-ori-wf-1-7139 Dynamical Systems (An Introduction to Complex Systems in Environment) fre 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" complex systems in environment environmental engineering dynamical systems non-linear dynamical system chaos Saddle-Node Bifurcation Pitchfork Bifurcation Hopf Bifurcation ingénierie de l’environnement système complexe LOMv1.0 collection LOMv1.0 4 LOMv1.0 texte LOMv1.0 image LOMv1.0 ressource interactive LOMv1.0 author BEGIN:VCARD VERSION:3.0 N:MEZEMATE;Yacine;;; FN:Yacine MEZEMATE EMAIL;TYPE=INTERNET: ORG:Ecole des Ponts ParisTech END:VCARD 2017-04-14 LOMv1.0 author BEGIN:VCARD VERSION:3.0 N:SCHERTZER;Daniel;;; FN:Daniel SCHERTZER EMAIL;TYPE=INTERNET: ORG:Ecole des Ponts ParisTech END:VCARD 2017-04-14 LOMv1.0 publisher BEGIN:VCARD VERSION:3.0 N:Ecole des Ponts ParisTech;;;; FN:Ecole des Ponts ParisTech EMAIL;TYPE=INTERNET: ORG:ENPC END:VCARD 2017-04-14 LOMv1.0 publisher BEGIN:VCARD VERSION:3.0 N:UNIT;;;; FN:UNIT EMAIL;TYPE=INTERNET: ORG:UNIT END:VCARD 2017-04-14 URI http://ori.unit-c.fr/uid/unit-ori-wf-1-7140 LOMv1.0 LOMFRv1.0 SupLOMFRv1.0 text/html https://hmco.enpc.fr/UNIT_ComplexSystems/~gen/3_DynamicalSystems/DynamicalSystems_web.publi/web/co/DynamicalSystems_web.html LOMv1.0 lecture LOMv1.0 exercise LOMv1.0 medium LOMv1.0 teacher LOMv1.0 learner LOMv1.0 manager LOMv1.0 higher education SupLOMFRv1.0 bac+3 fre LOMv1.0 no LOMv1.0 yes Cet ensemble de supports pédagogiques est la propriété, à parts égales, d’UNIT et de l'École des Ponts ParisTech. Il est régi par la licence logicielle GPL, dans sa version française CeCILL (http://www.cecill.info/licences/Licence_CeCILL-V1_VF.pdf). LOMv1.0 ispartof URI https://hmco.enpc.fr/complex-systems/ An Introduction to Complex Systems in Environment LOMv1.0 discipline Classification UNIT 104 Traitements de problèmes d'environnement Classification UNIT 103 Problèmes d'environnement LOMv1.0 discipline CDD 22e éd. 628.1 Techniques sanitaires et urbaines : approvisionnement en eau CDD 22e éd. 628.5 Contrôle de la pollution et techniques d'hygiène industrielle : sites pollués, sols, air CDD 22e éd. 363.7 Déchets, pollutions, polluants, bruit LOMv1.0 security level Projet OCW France tag-ocw Catalogue OCWC home-example unit-cofinance