- 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 398609, 5 pages
Fourteen Limit Cycles in a Seven-Degree Nilpotent System
1Guangxi Key Laboratory of Trusted Software, School of Computing Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, China
2Department of Mathematics, Hezhou University, Hezhou 542800, China
Received 13 August 2013; Accepted 30 October 2013
Academic Editor: Isaac Garcia
Copyright © 2013 Wentao Huang 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.
- A. F. Andreev, “Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point,” American Mathematical Society Translations, vol. 8, pp. 183–207, 1958.
- V. V. Amel’kin, N. A. Lukashevich, and A. P. Sadovskiĭ, Nonlinear Oscillations in Second Order Systems, Belarusian State University, Minsk, Russia, 1982, (Russian).
- V. G. Romanovskii, “On the cyclicity of the equilibrium position of the center or focus type of a certain system,” Vestnik St. Petersburg University: Mathematics, vol. 19, pp. 51–56, 1986.
- 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.
- 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 part,” Differential Equations, vol. 39, no. 2, pp. 155–164, 2003.
- 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.
- A. Algaba, C. García, and M. Reyes, “Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 314–323, 2009.
- Y. Liu and J. Li, “On third-order nilpotent critical points: integral factor method,” International Journal of Bifurcation and Chaos, vol. 21, no. 5, pp. 1293–1309, 2011.
- M. Han and V. G. Romanovski, “Limit cycle bifurcations from a nilpotent focus or center of planar systems,” Abstract and Applied Analysis, vol. 2012, Article ID 720830, 28 pages, 2012.
- Y. Liu and J. Li, “New study on the center problem and bifurcations of limit cycles for the Lyapunov system. I,” International Journal of Bifurcation and Chaos, vol. 19, no. 11, pp. 3791–3801, 2009.
- Y. Liu and J. Li, “New study on the center problem and bifurcations of limit cycles for the Lyapunov system. II,” International Journal of Bifurcation and Chaos, vol. 19, no. 9, pp. 3099–3807, 2009.
- Y. Liu and J. Li, “Bifurcations of limit cycles and center problem for a class of cubic nilpotent system,” International Journal of Bifurcation and Chaos, vol. 20, no. 8, pp. 2579–2584, 2010.
- F. Li, Y. Liu, and Y. Wu, “Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a seventh degree Lyapunov system,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 6, pp. 2598–2608, 2011.
- 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.