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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 762751, 8 pages
http://dx.doi.org/10.1155/2013/762751
Research Article

Limit Cycles and Isochronous Centers in a Class of Ninth Degree System

1School of Science, Linyi University, Linyi, Shandong 276005, China
2School of Science, Shaoyang University, Shaoyang, Hunan 422000, China

Received 15 April 2013; Accepted 3 October 2013

Academic Editor: Ruediger Landes

Copyright © 2013 Li Hongwei et al. 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

A class of ninth degree system is studied and the conditions ensuring that its five singular points can be centers and isochronous centers (or linearizable centers) at the same time by exact calculation and strict proof are obtained. What is more, the expressions of Lyapunov constants and periodic constants are simplified, and 21 limit circles could be bifurcated at least.