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

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  • Feng, Li

Abstract

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 system MATHEMATICA, 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 12 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 quintic Lyapunov systems, the result of Jiang et al. (2009) [18] was improved.

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  • Feng, Li, 2012. "Bifurcations of limit cycles in a quintic Lyapunov system with eleven parameters," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1417-1422.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1417-1422
    DOI: 10.1016/j.chaos.2012.07.012
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