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BIFURCATION OF LIMIT CYCLES FOR A FAMILY OF PERTURBED KUKLES DIFFERENTIAL SYSTEMS

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dc.creatorSALOMON REBOLLO PERDOMO
dc.creatorJOSÉ CLAUDIO VIDAL DÍAZ
dc.date2018
dc.date.accessioned2025-01-10T14:59:17Z
dc.date.available2025-01-10T14:59:17Z
dc.date.issued2018
dc.description.abstractWE CONSIDER AN INTEGRABLE NON-HAMILTONIAN SYSTEM, WHICH BELONGS TO THE QUADRATIC KUKLES DIFFERENTIAL SYSTEMS. IT HAS A CENTER SURROUNDED BY A BOUNDED PERIOD ANNULUS. WE STUDY POLYNOMIAL PERTURBATIONS OF SUCH A KUKLES SYSTEM INSIDE THE KUKLES FAMILY. WE APPLY AVERAGING THEORY TO STUDY THE LIMIT CYCLES THAT BIFURCATE FROM THE PERIOD ANNULUS AND FROM THE CENTER OF THE UNPERTURBED SYSTEM. FIRST, WE SHOW THAT THE PERIODIC ORBITS OF THE PERIOD ANNULUS CAN BE PARAMETRIZED EXPLICITLY THROUGH THE LAMBERT FUNCTION. LATER, WE PROVE THAT AT MOST ONE LIMIT CYCLE BIFURCATES FROM THE PERIOD ANNULUS, UNDER QUADRATIC PERTURBATIONS. MOREOVER, WE GIVE CONDITIONS FOR THE NON-EXISTENCE, EXISTENCE, AND STABILITY OF THE BIFURCATED LIMIT CYCLES. FINALLY, BY USING AVERAGING THEORY OF SEVENTH ORDER, WE PROVE THAT THERE ARE CUBIC SYSTEMS, CLOSE TO THE UNPERTURBED SYSTEM, WITH 1 AND 2 SMALL LIMIT CYCLES.
dc.formatapplication/pdf
dc.identifier.doi10.3934/dcds.2018182
dc.identifier.issn1553-5231
dc.identifier.issn1078-0947
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/9880
dc.languagespa
dc.publisherDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
dc.relation.uri10.3934/dcds.2018182
dc.rightsPUBLICADA
dc.titleBIFURCATION OF LIMIT CYCLES FOR A FAMILY OF PERTURBED KUKLES DIFFERENTIAL SYSTEMS
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
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