ABSTRACT In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.
Cite this paper
J. Jiang, "Limit Cycle Bifurcations in a Class of Cubic System near a Nilpotent Center," Applied Mathematics, Vol. 3 No. 7, 2012, pp. 772-777. doi: 10.4236/am.2012.37115.
 A. Andronov, E. Leontovich, I. Gordon and A. Maier, “Theory of Bifurcations of Dynamical Systems on a Plane,” Israel Program for Scientific Translations, Jerusalem, 1971.
 M. Han, “On Hopf Cyclicity of Planar Systems,” Journal of Mathematical Analysis and Applications, Vol. 245, No. 2, 2000, pp. 404-422. doi:10.1006/jmaa.2000.6758
 Y. A. Kuznetsov, “Elements of Applied Bifurcation Theory,” Springer-Verlag, New York, 1995.
 T. Carmon, R. Uzdin, C. Pigier, Z. Musslimani, M. Segev and A. Nepomnyashchy, “Rotating Propeller Solitons,” Physical Review Letters, Vol. 87, No. 14, 2001, p. 143901.
 J. Guckenheimer and P. Holmes, “Non-Linear Oscillations, Dynamical Systems and Bifurcation of Vector Fields,” Springer-Verlag, New York, 1983.
 B. D. Hassard, N. D. Kazarinoff and Y. H. Wan, “Theory and Applications of Hopf Bifurcation,” Cambridge University Press, Cambridge, 1981.
 S. Wiggins, “Global Bifurcations and Chaos: Analytical Methods,” Springer-Verlag, New York, 1988.
 M. Han J. Jiang and H. Zhu, “Limit Cycle Bifurcations in Near-Hamiltonian Systems by Perturbing a Nilpotent Center,” International Journal of Bifurcation and Chaos, Vol. 18, No. 10, 2008, pp. 3013-3027.