The Center Conditions and Bifurcation of Limit Cycles at the Degenerate Singularity of a Three‐Dimensional System

Shugang Song, Jingjing Feng and Qinlong Wang

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: We investigate multiple limit cycles bifurcation and center‐focus problem of the degenerate equilibrium for a three‐dimensional system. By applying the method of symbolic computation, we obtain the first four quasi‐Lyapunov constants. It is proved that the system can generate 3 small limit cycles from nilpotent critical point on center manifold. Furthermore, the center conditions are found and as weak foci the highest order is proved to be the fourth; thus we obtain at most 3 small limit cycles from the origin via local bifurcation. To our knowledge, it is the first example of multiple limit cycles bifurcating from a nilpotent singularity for the flow of a high‐dimensional system restricted to the center manifold.

Date: 2014
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https://doi.org/10.1155/2014/546243

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:546243

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