On a family of planar differential systems

  • Saad Eddine Hamizi Lab. de Math\'{e}matiques Appliqu\'{e}es, Universit\'{e} de Bejaia, 06000 Bejaia, Alg\'{e}rie.
  • Rachid Boukoucha University Bejaia, Algeria


We consider the family of the polynomial differential system. We prove that these systems are Darboux integrable. Moreover, we determine sufficient conditions for a polynomial differential system to possess an explicit algebraic or non-algebraic limit cycles. Concrete examples exhibiting the applicability of our result are introduced.