Limit cycles of discontinuous piecewise differential systems separated by a non–regular line and formed by an arbitrary linear center and an arbitrary quadratic center

Abstract

This 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.