Effective construction of Poincaré-Bendixson regions
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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.
Is part ofJournal Of Applied Analysis And Computation, 2017, vol. 7, núm. 4, p. 1549-1569
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Giacomini, Héctor; Grau Montaña, Maite (Elsevier, 2015)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 conics. We present ...
Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Rocky Mountain Mathematics Consortium, 2006)In this work we consider rational ordinary differential equations dy/dx = Q(x, y)/P(x, y), with Q(x, y) and P(x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for ...
Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Cambridge University Press, 2007)We study a planar polynomial differential system, given by . We consider a function , where gi(x) are algebraic functions of with ak(x) and algebraic functions, A0(x,y) and A1(x,y) do not share any common factor, h2(x) is ...