Limit cycles for 3-monomial differential equations

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Abstract

© 2015 Elsevier Inc. We study planar polynomial differential equations that in complex coordinates write as z ˙=Az+Bzkz-l+Czmz-n. We prove that for each p∈N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case z ˙=Az+Bz-+Czmz-n, which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.
Original languageEnglish
Pages (from-to)735-749
JournalJournal of Mathematical Analysis and Applications
Volume428
Issue number2
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Abelian integrals
  • Bifurcations
  • Homogeneous nonlinearities
  • Limit cycles
  • Z<inf>q</inf>-equivariant symmetry

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