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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Center Conditions and Bifurcations of Limit Cycles in a Quartic Lyapunov System
verfasst von : Dexue Zhang
Erschienen in: Practical Applications of Intelligent Systems
Verlag: Springer Berlin Heidelberg
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In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quartic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 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 8 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 quartic Lyapunov systems.