On the limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 3 via the averaging method

Jaume Llibre, Claudia Valls

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Abstract

We study the limit cycles of a class of cubic polynomialdifferential systems in the plane and their global shape using the averaging theory. More specifically, we analyze the global shape of the limit cycles which bifurcate: first, from a Hopf bifurcation; second, from periodic orbits of the linear center ẋ = -y, ẏ = x; and finally from periodic orbits of the cubic centers ẋ = -yh(x, y), ẏ = xh(x, y) where h(x, y) = 0 is a conic. The perturbation of these systems is made inside the class of cubic polynomial differential systems havingnon quadratic terms. © Watnam Press.
Original languageEnglish
Pages (from-to)453-473
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume17
Issue number4
Publication statusPublished - 13 Sep 2010

Keywords

  • Averaging theory
  • Cubic polynomial differential systems
  • Cubic vector fields
  • Limit cycles

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