Localizing limit cycles: From numeric to analytical results

Armengol Gasull, Héctor Giacomini, Maite Grau

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© Springer Nature Switzerland AG 2018. This note presents the results of [4]. It 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
Title of host publicationTrends in Mathematics
Number of pages4
ISBN (Electronic)2297-024X
Publication statusPublished - 1 Jan 2018


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


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