As we know, Bautin proved that a focus of a quadratic system has order at most 3. We give a new and simple proof to this well-known result by using an elementary method. We also use the elementary method to give a necessary and sufficient condition for a quadratic system to have a center.
Chaos, Solitons and Fractals,
Vol. 31, no. 1 (Jan 2007), pp. 218-223