Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2014 (2014), Article ID 546243, 8 pages.
The Center Conditions and Bifurcation of Limit Cycles at the Degenerate Singularity of a Three-Dimensional System
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.
J. Appl. Math., Volume 2014 (2014), Article ID 546243, 8 pages.
First available in Project Euclid: 2 March 2015
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Song, Shugang; Feng, Jingjing; Wang, Qinlong. The Center Conditions and Bifurcation of Limit Cycles at the Degenerate Singularity of a Three-Dimensional System. J. Appl. Math. 2014 (2014), Article ID 546243, 8 pages. doi:10.1155/2014/546243. https://projecteuclid.org/euclid.jam/1425305889