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Limit cycles in a sextic Lyapunov system

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Abstract

Employing the inverse integral factor method, the first 13 quasi-Lyapunov constants for the three-order nilpotent critical point of a sextic Lyapunov system are deduced with the help of MATHEMATICS. Furthermore, sufficient and necessary center conditions are obtained, and there are 13 small amplitude limit cycles, which could be bifurcated from the three-order nilpotent critical point. Henceforth, we give a lower bound of limit cycles, which could be bifurcated from the three-order nilpotent critical point of sextic Lyapunov systems. At last, an example is given to show that there exists a sextic system, which has 13 limit cycles.

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Acknowledgements

This research is partially supported by the National Nature Science Foundation of China (11201211, 61273012) and Nature Science Foundation of Shandong Province (ZR2012AL04).

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  1. School of Science, Linyi University, Linyi, 276005, Shandong, P.R. China

    Hongwei Li

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  1. Hongwei Li
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Correspondence to Hongwei Li.

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Li, H. Limit cycles in a sextic Lyapunov system. Nonlinear Dyn 72, 555–559 (2013). https://doi.org/10.1007/s11071-012-0733-3

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  • DOI: https://doi.org/10.1007/s11071-012-0733-3

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