We will introduce Mironenko’s method to discuss the Poincaré center-focus problem, and compare the methods of Lyapunov and Mironenko. We apply the Mironenko method to discuss the qualitative behavior of solutions of some planar polynomial differential systems and derive the sufficient conditions for a critical point to be a center.
"A New Method for Research on the Center-Focus Problem of Differential Systems." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/926538