The limit cycle problem of quadratic system $($Ⅲ$)_{n=0}$ is studied in this paper. By using Hopf bifurcation, the parameter regions for which limit cycles exist are obtained, and for the rest regions of parameters, the nonexistance of limit cycles is proved by using qualitative methods. A positive answer for an important conjecture in [2, \S9] is also given and it is shown that our results are more complete than that obtained in paper [5]. |