Phase planes and bifurcations in planar linear-quadratic differential systems with a pseudo-focus

Abstract

Our thesis isdividedinthreeparts,thefirstpartconsistsinsolvingthesecondpartofthe extended 16thHilbertproblemforaclassofdiscontinuouspiecewisedifferentialsystems.The second partfocusesonfindingthemaximumnumberoflimitcyclesofsmallamplitudewhichis called thecyclictyproblem,andthethirdpartwewereabletofindtheglobalphaseportraitsand the bifurcationsetsforsomespecificfamiliesofdiscontinuouspiecewisequadraticdifferential systems, characterizedbyhavingapseudo-centreattheorigin