Stability of certain planar unbounded polycycles

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Abstract

We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.
Original languageEnglish
Pages (from-to)332-351
JournalJournal of Mathematical Analysis and Applications
Volume269
Issue number1
DOIs
Publication statusPublished - 1 May 2002

Keywords

  • Bifurcation of limit cycles
  • Polycycle
  • Polynomial vector field
  • Stability

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