Effective construction of Poincaré-Bendixson regions

Armengol Gasull, Héctor Giacomini, Maite Grau

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2017, Wilmington Scientific Publisher. All rights reserved. This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré–Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Liénard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.
Original languageEnglish
Pages (from-to)1549-1569
JournalJournal of Applied Analysis and Computation
Volume7
Issue number4
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Bendixson region
  • Bifurcation
  • Limit cycle
  • Planar differential system
  • Poincaré
  • Transversal curve

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