We consider the one-parameter family of planar quantic system,, introduced by A.Bacciotti in1985. Introduced by A.Bacciotti in1985. It is known that it has at most one limit cycle and that it can exist only when the parameter m is in . By using the Bendixson-Dulac theorem, we give a new uni?ed proof of all the previous results. We shrink this interval to (0.547, 0.6) and we prove the hyperbolicity of the limit cycle. Furthermore, we consider the question of the existence of polycycles. The main interest and di?culty for studying this family is that it is not a semi-complete family of rotated vector ?elds. When the system has a limit cycle, we also determine explicit lower bounds of basin of attraction of the origin. Finally, we answer an open question about the change of stability of the origin for an extension of the above systems. A. Bacciotti, during a conference about the stability of analytic dynamical systems held in Florence in 1985, proposed to study the stability of the origin of the following quantic system (1) Two years later, Galeotti and Gori published an extensive study of (1). They proved that system (1) has no limit cycles when , otherwise, it has at most one. Their proofs are mainly based on the study of the stability of the limit cycles which is controlled by the sign of its characteristic exponent, together with a transformation of the system using a special type of adapted polar coordinates. Their proof of the uniqueness of the limit cycle does not cover its hyperbolicity. In this thesis, we re?ne the above results. To guess which is the actual bifurcation diagram we ?rst did a numerical study, obtaining the following results. It seems that there exists a value uch that: (i) System (1) has no limit cycles if . Moreover, for it has a heteroclinic polycycle formed by the separatrices of the two saddle points located at . (ii) For the system has exactly one unstable limit cycle.