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2014 The Center Conditions and Bifurcation of Limit Cycles at the Degenerate Singularity of a Three-Dimensional System
Shugang Song, Jingjing Feng, Qinlong Wang
J. Appl. Math. 2014: 1-8 (2014). DOI: 10.1155/2014/546243

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.

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Shugang Song. Jingjing Feng. Qinlong Wang. "The Center Conditions and Bifurcation of Limit Cycles at the Degenerate Singularity of a Three-Dimensional System." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/546243

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131683
MathSciNet: MR3232919
Digital Object Identifier: 10.1155/2014/546243

Rights: Copyright © 2014 Hindawi

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