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Title

Bifurcation of limit cycles for a class of cubic polynomial system having a nilpotent singular point
Author

Xuejun Pan
Journal / Anthology

Applied Mathematics and Computation
Year: 2011
Volume: 218
Issue: 4
Page range: 1161-1165
Description

In this paper, center conditions and bifurcations of limit cycles for a class of cubic polynomial system in which the origin is a nilpotent singular point are studied. A recursive formula is derived to compute quasi-Lyapunov constant. Using the computer algebra system Mathematica, the first seven quasi-Lyapunov constants of the system are deduced. At the same time, the conditions for the origin to be a center and 7-order fine focus are derived respectively. A cubic polynomial system that bifurcates seven limit cycles enclosing the origin (node) is constructed.
Subject

*Unclassified