Baymout, Louiza2024-06-232024-06-232024-06-11MD/24http://10.10.1.6:4000/handle/123456789/5036This thesisconsistsoftwoimportantparts,thefirstoneisdevotedtothe study oftheupperboundonthenumberoflimitcyclesthatcanbecreatedfrom three differentnon-linearfamiliesofdiscontinuouspiecewisedifferentialsystems separated byaregularline. The secondpartfocusesonthestudyoftheexistenceandthemaximumnumber of limitcyclesofaclassofnon-lineardiscontinuouspiecewisedifferentialsystems but inthiscaseweuseanirregularlineastheseparationcurveinsteadofregular line.This thesisconsistsoftwoimportantparts,thefirstoneisdevotedtothe study oftheupperboundonthenumberoflimitcyclesthatcanbecreatedfrom three differentnon-linearfamiliesofdiscontinuouspiecewisedifferentialsystems separated byaregularline. The secondpartfocusesonthestudyoftheexistenceandthemaximumnumber of limitcyclesofaclassofnon-lineardiscontinuouspiecewisedifferentialsystems but inthiscaseweuseanirregularlineastheseparationcurveinsteadofregular line.enDiscontinuouspiecewisedifferentialsystem,limitcycle,linearcenter, (regular/ irregular)line,quadraticcenter,isochronouscenter,nilpotentcenterDiscontinuouspiecewisedifferentialsystem,limitcycle,linearcenter, (regular/ irregular)line,quadraticcenter,isochronouscenter,nilpotentcenterLimit cycles of discontinuous piecewise differential systems separated by a non–regular line and formed by an arbitrary linear center and an arbitrary quadratic centerThesis