Effective construction of Poincaré-Bendixson regions

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Date
2017
Authors
Gasull, Armengol
Giacomini, Héctor
Grau Montaña, MaiteGrau Montaña, Maite - ORCID ID
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cc-by (c) Gasull et al., 2017
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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.
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Journal Of Applied Analysis And Computation, 2017, vol. 7, núm. 4, p. 1549-1569