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
| dc.contributor.author | Baymout, Louiza | |
| dc.date.accessioned | 2024-06-23T12:24:47Z | |
| dc.date.available | 2024-06-23T12:24:47Z | |
| dc.date.issued | 2024-06-11 | |
| dc.description.abstract | This thesisconsistsoftwoimportantparts,thefirstoneisdevotedtothe study oftheupperboundonthenumberoflimitcyclesthatcanbecreatedfrom three differentnon-linearfamiliesofdiscontinuouspiecewisedifferentialsystems separated byaregularline. The secondpartfocusesonthestudyoftheexistenceandthemaximumnumber of limitcyclesofaclassofnon-lineardiscontinuouspiecewisedifferentialsystems but inthiscaseweuseanirregularlineastheseparationcurveinsteadofregular line. | en_US |
| dc.description.abstract | This thesisconsistsoftwoimportantparts,thefirstoneisdevotedtothe study oftheupperboundonthenumberoflimitcyclesthatcanbecreatedfrom three differentnon-linearfamiliesofdiscontinuouspiecewisedifferentialsystems separated byaregularline. The secondpartfocusesonthestudyoftheexistenceandthemaximumnumber of limitcyclesofaclassofnon-lineardiscontinuouspiecewisedifferentialsystems but inthiscaseweuseanirregularlineastheseparationcurveinsteadofregular line. | en_US |
| dc.identifier.issn | MD/24 | |
| dc.identifier.uri | http://10.10.1.6:4000/handle/123456789/5036 | |
| dc.language.iso | en | en_US |
| dc.publisher | UNIVERSITY BBA | en_US |
| dc.subject | Discontinuouspiecewisedifferentialsystem,limitcycle,linearcenter, (regular/ irregular)line,quadraticcenter,isochronouscenter,nilpotentcenter | en_US |
| dc.subject | Discontinuouspiecewisedifferentialsystem,limitcycle,linearcenter, (regular/ irregular)line,quadraticcenter,isochronouscenter,nilpotentcenter | en_US |
| dc.title | 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 | en_US |
| dc.type | Thesis | en_US |
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- This thesis devotedtosolvethesecondpartofthesixteenthHilbertproblemfor twotypesofplanarPWSdependingonthenatureoftheseparationcurve,the first typeseparatedbytheregularline Σr and thesecondtypeseparatedbytheirregular line Σi . Firstlywhentheseparationcurveistheregularline Σr westudythelimitcyclesfor PWSformedeitherbylinearandcubicdifferentialcentersoronlycubicdifferential centersineachregion.Weanalyzethemaximumnumberoflimitcyclesthatcanbe bifurcatefromthefivefamiliesofPWSbyusingstandardtechniquessuchasBézout theorem, Resultanttheory,orthemaximumnumberoftheintersectionpointsbetween the graphicsofnon-algebraicfunctions.Consequentlywedemonstratethatwhenthe separationcurveisaregularline,thereexistfamiliesofPWSwithatmostfourlimit cycles. Wealsoprovideexampleswhichconfirmthatthisupperboundisreached. Secondlywhenweconsidertheirregularseparationcurve Σi weexaminethelimitcy- cles fortheclassofPWSformedbylinearandquadraticdifferentialcenters.Weanalyze the maximumnumberoflimitcyclesthatcanbecreatedfromthisclassofPWSbyus- ing themaximumnumberofintersectionpointsbetweenthegraphicsofnon-algebraic functions. Weprovethateightisthemaximumnumberoflimitcyclesforthisclassof systems. Thenwedemonstratehowthenatureoftheseparationcurveaffects thismax- imumnumberforplanarPWS.Additionallyweprovideexampleswithexactlysixlimit cycles. While thisstudyhasprovidedvaluableinsightsintothebehaviorofsomenon-linear PWS,thereremainsavastandpromisingfrontierawaitingexplorationintherealmof non-linear PWS.Additionallythisworkcouragouslygiveslighttotheusesofseparation curvesbeyondregularlinesthataffect thedynamicswithinPWS.
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