Abstract
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.
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Zhang, D. (2011). Center Conditions and Bifurcations of Limit Cycles in a Quartic Lyapunov System. In: Wang, Y., Li, T. (eds) Practical Applications of Intelligent Systems. Advances in Intelligent and Soft Computing, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25658-5_36
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DOI: https://doi.org/10.1007/978-3-642-25658-5_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25657-8
Online ISBN: 978-3-642-25658-5
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