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Title

The center conditions and bifurcation of limit cycles at the infinity for a cubic polynomial system
Authors

Lina Zhang
Yirong Liu
Xuejiao Jiang
Journal / Anthology

Applied Mathematics and Computation
Year: 2011
Volume: 218
Issue: 4
Page range: 1360-1370
Description

In this paper, the problem of center conditions and bifurcation of limit cycles at the infinity for a class of cubic systems are investigated. The method is based on a homeomorphic transformation of the infinity into the origin, the first 21 singular point quantities are obtained by computer algebra system Mathematica, the conditions of the origin to be a center and a 21st order fine focus are derived, respectively. Correspondingly, we construct a cubic system which can bifurcate seven limit cycles from the infinity by a small perturbation of parameters. At the end, we study the isochronous center conditions at the infinity for the cubic system.
Subject

*Unclassified