Abstract and Applied Analysis
Volume 2013 (2013), Article ID 575390, 19 pages
http://dx.doi.org/10.1155/2013/575390
Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Received 5 October 2012; Accepted 21 November 2012
Academic Editor: Yonghui Xia
Copyright © 2013 Yanqin Xiong and Maoan Han. 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
This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we investigate the maximal number of limit cycles that bifurcate from a global center up to first order of .