ON LIMIT CYCLES OF PLANE QUADRATIC SYSTEMS

This paper gives new conditions of limit-cycles existence for plane quadratic systems （Theorems1 and 2） with global observation. Thus, in the parametric space of dimension 12 consisting of thecoefficients of quadratic systems, we find such a manifold of dimension 12 （Theorem 5） and amanifold of dimension 11 （Theorem 6） that the corresponding plane quadratic systems have at leastfour limit cycles. It is pointed out that the sign of the third Liapunov constant in [1] is made awrong calculation. The right result is V= λλ（λ- λ）（λ- λλ+ 2λ）,which affects the existence of one limit cycle.