- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 861052, 5 pages
Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points
School of Science, Linyi University, Shandong, Linyi 276005, China
Received 17 December 2012; Accepted 2 February 2013
Academic Editor: Chuangxia Huang
Copyright © 2013 Feng Li and Jianlong Qiu. 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.
- Q. Zhang and Y. Liu, “A cubic polynomial system with seven limit cycles at infinity,” Applied Mathematics and Computation, vol. 177, no. 1, pp. 319–329, 2006.
- Y. Liu and W. Huang, “Seven large-amplitude limit cycles in a cubic polynomial system,” International Journal of Bifurcation and Chaos, vol. 16, no. 2, pp. 473–485, 2006.
- Q. Zhang and Y. Liu, “A quintic polynomial differential system with eleven limit cycles at the infinity,” Computers & Mathematics with Applications, vol. 53, no. 10, pp. 1518–1526, 2007.
- Q. Zhang, G. Weihua, and Y. Liu, “Bifurcation of limit cycles at the equator for a class of polynomial differential system,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 1042–1047, 2009.
- A. F. Andreev, A. P. Sadovskiĭ, and V. A. Tsikalyuk, “The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear pact,” Differential Equations, vol. 39, no. 2, pp. 155–164, 2003.
- M. J. Álvarez and A. Gasull, “Monodromy and stability for nilpotent critical points,” International Journal of Bifurcation and Chaos, vol. 15, no. 4, pp. 1253–1265, 2005.
- M. J. Álvarez and A. Gasull, “Generating limit cycles from a nilpotent critical point via normal forms,” Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 271–287, 2006.
- F. Li, “Bifurcations of limit cycles in a quintic Lyapunov system with eleven parameters,” Chaos, Solitons & Fractals, vol. 45, no. 11, pp. 1417–1422, 2012.
- F. Li, Y. Liu, and H. Li, “Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system,” Mathematics and Computers in Simulation, vol. 81, no. 12, pp. 2595–2607, 2011.
- Y. Liu and J. Li, Some Classical Problems about Planar Vector Fields, Science Press, Beijing, China, 2010.