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The Scientific World Journal
Volume 2014, Article ID 705703, 12 pages
Research Article

The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China

Received 4 December 2013; Accepted 3 March 2014; Published 26 March 2014

Academic Editors: B. Hong and J. Li

Copyright © 2014 Yanan Jiang 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.


We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in .