- 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 482850, 7 pages
The Number of Limit Cycles of a Polynomial System on the Plane
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Received 23 April 2013; Accepted 16 June 2013
Academic Editor: Csaba Varga
Copyright © 2013 Chao Liu 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.
- V. I. Arnold, “Some unsolved problems in the theory of differential equations and mathematical physics,” Russian Mathematical Surveys, vol. 44, pp. 157–171, 1989.
- J. Li, “Hilbert's 16th problem and bifurcations of planar polynomial vector fields,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 1, pp. 47–106, 2003.
- H. Giacomini, J. Llibre, and M. Viano, “On the nonexistence, existence and uniqueness of limit cycles,” Nonlinearity, vol. 9, no. 2, pp. 501–516, 1996.
- J. Llibre, J. S. Pérez del Río, and J. A. Rodríguez, “Averaging analysis of a perturbated quadratic center,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 46, no. 1, pp. 45–51, 2001.
- G. Xiang and M. Han, “Global bifurcation of limit cycles in a family of polynomial systems,” Journal of Mathematical Analysis and Applications, vol. 295, no. 2, pp. 633–644, 2004.
- A. Buică and J. Llibre, “Limit cycles of a perturbed cubic polynomial differential center,” Chaos, Solitons and Fractals, vol. 32, no. 3, pp. 1059–1069, 2007.
- B. Coll, J. Llibre, and R. Prohens, “Limit cycles bifurcating from a perturbed quartic center,” Chaos, Solitons & Fractals, vol. 44, no. 4-5, pp. 317–334, 2011.
- A. Atabaigi, N. Nyamoradi, and H. R. Z. Zangeneh, “The number of limit cycles of a quintic polynomial system,” Computers & Mathematics with Applications, vol. 57, no. 4, pp. 677–684, 2009.
- A. Gasull, J. T. Lázaro, and J. Torregrosa, “Upper bounds for the number of zeroes for some Abelian integrals,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 13, pp. 5169–5179, 2012.
- A. Gasull, R. Prohens, and J. Torregrosa, “Bifurcation of limit cycles from a polynomial non-global center,” Journal of Dynamics and Differential Equations, vol. 20, no. 4, pp. 945–960, 2008.
- G. Xiang and M. Han, “Global bifurcation of limit cycles in a family of multiparameter system,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 14, no. 9, pp. 3325–3335, 2004.
- A. Gasull, C. Li, and J. Torregrosa, “Limit cycles appearing from the perturbation of a system with a multiple line of critical points,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 75, no. 1, pp. 278–285, 2012.