Sur la théorie des cycles limites

Abstract

Ce m´emoire s’articule autour de l’´etude qualitative des syst`emes diff´erentiels, qui a pour but de trouver les propri´et´es de leurs solutions(comme les points d’´equilibres, les courbes invariantes et les solutions p´eriodiques), sans connaitre la solution explicite qui est g´en´eralement difficile. Nous nous sommes int´eress´es `a la construction de classes des syst`emes diff´erentiels planaires, et des syst`emes de type Kolmogorov, o`u nous avons ´etudi´e l’int´egrabilit´e et l’existence des cycles limites. , ...In this dissertation, we are interested in on the qualitative study of differential systems, which aims to find the properties of their solutions (such as equilibrium points, invariant curves and periodic solutions), without pursuing the explicit resolution that is generally difficult. We are interested in the construction of classes of planar differential systems, and Kolmogorov-type systems, where we studied the integrability and existence of limit cycles.