A new criterion for controlling the number of limit cycles of some generalized liénard equations

Armengol Gasull, Hector Giacomini

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)

Abstract

We consider a class of planar differential equations which include the Liénard differential equations. By applying the Bendixson-Dulac Criterion for ℓ-connected sets we reduce the study of the number of limit cycles for such equations to the condition that a certain function of just one variable does not change sign. As an application, this method is used to give a sharp upper bound for the number of limit cycles of some Liénard differential equations. In particular, we present a polynomial Liénard system with exactly three limit cycles. © 2002 Elsevier Science (USA).
Original languageEnglish
Pages (from-to)54-73
JournalJournal of Differential Equations
Volume185
Issue number1
DOIs
Publication statusPublished - 10 Oct 2002

Keywords

  • Liénard equation
  • Limit cycle
  • Ordinary differential equation

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