Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers

Jaume Llibre, Yun Tian

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Abstract

© 2018 World Scientific Publishing Company. In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree 4 surrounding a center. We show that there exists only one family of such systems satisfying that an algebraic limit cycle of degree 4 can bifurcate from the period annulus of the mentioned center under quadratic perturbations.
Original languageEnglish
Article number1850145
JournalInternational Journal of Bifurcation and Chaos
Volume28
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • bifurcation from center
  • cyclicity of the period annulus
  • limit cycle
  • periodic orbit
  • Quadratic vector fields

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    Llibre, J., & Tian, Y. (2018). Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers. International Journal of Bifurcation and Chaos, 28, [1850145]. https://doi.org/10.1142/S0218127418501456