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Advances in Mathematical Physics
Volume 2015, Article ID 479480, 11 pages
Research Article

Existence of Center for Planar Differential Systems with Impulsive Perturbations

Department of Mathematics, Chuxiong Normal University, Chuxiong, Yunnan 675000, China

Received 4 March 2015; Accepted 4 April 2015

Academic Editor: Ming Mei

Copyright © 2015 Dengguo Xu. 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.


We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.