Limit cycles and invariant centers for an extended Kukles system

  • Zhenhai Liu, Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation and College of Sciences, Guangxi University for Nationalities, Nanning Guangxi 530006, P.R. China,
  • Iván Szántó, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Departamento de Matematica, Casilla 110-V, Valparaiso, Chile,


A class of polynomial systems of odd degree with limit cycles, invariant centers and invariant straight lines, is examined. The limit cycles can be obtain as a bifurcation of a non hyperbolic focus at the origin as Hopf bifurcations. We will also obtain the necessary and sufficient conditions for the critical point at the interior of bounded region to be a center.

Vol. 18 (2017), No. 2, pp. 947-952
DOI: 10.18514/MMN.2017.2043

Download: MMN-2043