Algebraic limit cycles in polynomial systems of differential equations

Jaume Llibre, Yulin Zhao

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4. © 2007 IOP Publishing Ltd.
Original languageEnglish
Pages (from-to)14207-14222
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
DOIs
Publication statusPublished - 23 Nov 2007

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