Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems-中国期刊网

摘要 Inthispaper,weinvestigatethenumber,locationandstabilityoflimitcyclesinaclassofperturbedpolynomialsystemswith(2n+1)or(2n+2)-degreebyconstructingdetectionfunctionandusingqualitativeanalysis.Weshowthatthereareatmostnlimitcyclesintheperturbedpolynomialsystem,whichissimilartotheresultofPerkoin[8]byusingMelnikovmethod.Forn=2,weestablishthegeneralconditionsdependingonpolynomial'scoefficientsforthebifurcationlocationandstabilityoflimitcycles.Thebifurcationparametervalueoflimitcyclesin[5]isalsoimprovedbyus.Whenn=3thesufficientandnecessaryconditionsfortheappearanceof3limitcyclesaregiven.Twonumericalexamplesforthelocationandstabilityoflimitcyclesareusedtodemonstrateourtheoreticalresults.

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Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems

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Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems

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