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Abstract and Applied Analysis
Volume 2014, Article ID 926538, 5 pages
http://dx.doi.org/10.1155/2014/926538
Research Article

A New Method for Research on the Center-Focus Problem of Differential Systems

School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Received 13 December 2013; Accepted 17 February 2014; Published 20 March 2014

Academic Editor: Douglas R. Anderson

Copyright © 2014 Zhengxin Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.