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Bifurcations of limit cycles in a quintic Lyapunov system with eleven parameters

Li Feng
Journal / Anthology

Chaos, Solitons & Fractals
Year: 2012
Volume: 45
Page range: 14171422

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra systemMATHEMATICA, the first 12 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 12smallamplitude limit cycles created fromthe three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems, the result of Jiang et al. (2009) [18] was improved.