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Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov system

Yusen Wu
Organization: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang
P. Li
Haibo Chen
Journal / Anthology

Communications in Nonlinear Science and Numerical Simulation
Year: 2012
Volume: 17
Issue: 1
Page range: 292-304

In the present paper, for the three-order nilpotent critical point of a cubic Lyapunov system, the center problem and bifurcation of limit cycles are investigated. With the help of computer algebra system-MATHEMATICA, the first 7 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact of there exist 7 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for cubic Lyapunov systems.  2011 Elsevier B.V. All rights reserved.