Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2

J. Llibre; B. D. Lopes; J. R. De Moraes

doi:https://doi.org/10.1016/j.amc.2015.10.079

Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2

J. Llibre, B. D. Lopes, J. R. De Moraes

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

© 2015 Elsevier Inc. All rights reserved. We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. The computations has been done with the help of the algebraic manipulator Mathematica.

Original language	English
Pages (from-to)	47-54
Journal	Applied Mathematics and Computation
Volume	274
DOIs	https://doi.org/10.1016/j.amc.2015.10.079
Publication status	Published - 1 Feb 2016

Keywords

Averaging method
Limit cycle
Polynomial vector field
Weight-homogeneous differential system

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abstract = "{\textcopyright} 2015 Elsevier Inc. All rights reserved. We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. The computations has been done with the help of the algebraic manipulator Mathematica.",

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N2 - © 2015 Elsevier Inc. All rights reserved. We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. The computations has been done with the help of the algebraic manipulator Mathematica.

AB - © 2015 Elsevier Inc. All rights reserved. We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. The computations has been done with the help of the algebraic manipulator Mathematica.

KW - Averaging method

KW - Limit cycle

KW - Polynomial vector field

KW - Weight-homogeneous differential system

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