EFFECTIVE CONSTRUCTION OF POINCAR&#201;-BENDIXSON REGIONS

Armengol Gasull; Héctor Giacomini; Maite Grau

doi:10.11948/2017094

2017 Volume 7 Issue 4

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Armengol Gasull, Héctor Giacomini, Maite Grau. EFFECTIVE CONSTRUCTION OF POINCARÉ-BENDIXSON REGIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1549-1569. doi: 10.11948/2017094

Citation:

Armengol Gasull, Héctor Giacomini, Maite Grau. EFFECTIVE CONSTRUCTION OF POINCARÉ-BENDIXSON REGIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1549-1569. doi: 10.11948/2017094

EFFECTIVE CONSTRUCTION OF POINCARÉ-BENDIXSON REGIONS

1 Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain;
2 Laboratoire de Mathématiques et Physique Théorique. C. N. R. S. UMR 7350., Faculté des Sciences et Techniques. Université de Tours, Parc de Grandmont 37200 Tours, France;
3 Departament de Matemàtica, Universitat de Lleida, Avda. Jaume Ⅱ, 69;
25001 Lleida, Catalonia, Spain

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Abstract

Abstract

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.
- Transversal curve /
- Poincaré-Bendixson region /
- limit cycle /
- bifurcation /
- planar differential system
MSC: 34C05;34C07;37C27;34C25;34A34

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References

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