2017
DOI: 10.15388/na.2017.4.1
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A note on the existence and construction of Dulac functions

Abstract: We provide sufficient conditions on the components of a vector field, which ensure the existence of Dulac functions depending on special functions for such vector field. We also present some applications and examples in order to illustrate our results.

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Cited by 4 publications
(4 citation statements)
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“…From the above relation, we notice that ( 1 , 2 ) does not deviate in sign and is not identical to zero in the interior of the positive first quadrant of the 1 , 2 plane. Therefore, it follows by the Bendixon-Dulac criteria [20] that there is no closed orbit, which implies that the system has no limit cycle in the interior of X12 and that ends the proof.…”
Section: Global Analysismentioning
confidence: 72%
“…From the above relation, we notice that ( 1 , 2 ) does not deviate in sign and is not identical to zero in the interior of the positive first quadrant of the 1 , 2 plane. Therefore, it follows by the Bendixon-Dulac criteria [20] that there is no closed orbit, which implies that the system has no limit cycle in the interior of X12 and that ends the proof.…”
Section: Global Analysismentioning
confidence: 72%
“…El siguiente resultado es uno de los dos resultados principales publicados en [22], en el cual se plantea lo siguiente Teorema 3.7. Sea Ω una región simplemente conexa en un conjunto abierto, supóngase un campo vectorial de la siguiente forma:…”
Section: Criterios Particulares Y Otros Criterios 331 El Problema 16hunclassified
“…A continuación se presenta el retrato fase del campo vectorial asociado al modelo (4.7) (ver Figura 4.4), los parámetros utilizados para obtener el retrato fase son: Ejemplo 4.5. Considerése el siguiente modelo de mutualismo y captura analizado en [22].…”
Section: Casos Particulares De Modelos De Interacciones Entre Especiesunclassified
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