Abstract
In this paper, bifurcation of small amplitude limit cycles from the degenerate equilibrium of a three-dimensional system is investigated. Firstly, the method to calculate the focal values at nilpotent critical point on center manifold is discussed. Then an example is studied, by computing the quasi-Lyapunov constants, the existence of at least 4 limit cycles on the center manifold is proved. In terms of degenerate singularity in high-dimensional systems, our work is new.
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Supported by Natural Science Foundation of China grants 11461021, 11261013, Nature Science Foundation of Guangxi (2015GXNSFAA139011), the Scientific Research Foundation of Guangxi Education Department (ZD2014131) and Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Processing.
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Wang, Ql., Huang, Wt. & Liu, Yr. Multiple limit cycles bifurcation from the degenerate singularity for a class of three-dimensional systems. Acta Math. Appl. Sin. Engl. Ser. 32, 73–80 (2016). https://doi.org/10.1007/s10255-015-0510-4
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DOI: https://doi.org/10.1007/s10255-015-0510-4