Hichem, Laib2022-03-142022-03-142020http//localhost:8080/jspui/handle/123456789/2044In this work, we first study the limit cycles which can bifurcate from the periodic orbits of the quadratic isochronous centers 𝒙̇ = −𝒚 + 𝒙 𝟐 , 𝒚̇ = 𝒙 + 𝒙𝒚, and 𝒙̇ = −𝒚 + 𝒙 𝟐 − 𝒚 𝟐 , 𝒚̇ = 𝒙 + 𝟐𝒙𝒚, when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y  0 . In the second part of this work, we use the averaging method to study the maximum number of limit cycles of the differential system 𝒙̇ = −𝒚 + 𝒙𝒚 + ∑𝜺 𝒌 ∑ 𝒂𝒊,𝒋 (𝒌) 𝒙 𝒊𝒚 𝒋 𝒊+𝒋=𝟐 𝟐 𝒌=𝟏 , 𝒚̇ = 𝒙 + 𝒚 𝟐 + ∑𝜺 𝒌 ∑ 𝒃𝒊,𝒋 (𝒌) 𝒙 𝒊𝒚 𝒋 𝒊+𝒋=𝟐 𝟐 𝒌=𝟏 , where  is a sufficiently small parameter. Keywords: Limit cycle, quadratic isochrone center, differential system, averaging methodfrLimit cycle, quadratic isochrone center, differential system, averaging methodCycle limite, centre isochrone quadratique, système différentiel, méthode de la moyennisation.Thesis