2004•Journal of Central South University of Technology(Natural Science)Requires access
A cubic polynomial system with six limit cycles at infinity
Wentao Huang, Yirong Liu
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Abstract
The bifurcation of limit cycles at infinity for a class of cubic polynomial systems was studied in the paper. A recursive formula is derived to compute singular point values at infinity. (Using) the recursive formula and computer algebra system-Mathematica, the first six singular point values at infinity of the system are given. The conditions for infinity to be a center and the highest degree fine focus are derived, respectively. A cubic system that bifurcates six limit cycles from infinity is obtained. The exact positions of these limit cycles are also pointed out.