Some criteria for the existence of limit cycles for quadratic vector fields

In this paper we consider real quadratic systems. We present new criteria for the existence and uniqueness of limit cycles for such systems by using Darbouxian particular solutions. Some results are based on the study of such systems in CP2.We also generalize the well-know result of Bautin on the nonexistence of limit cycles for quadratic Lotka–Volterra systems.  2003 Elsevier Science (USA). All rights reserved