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Title

Bifurcation of limit cycles at the equator
Authors

Qi Zhang
Zhao Zhengquan
Gui Weihua
Journal / Anthology

APPLIED MATHEMATICS AND COMPUTATION
Year: 2009
Volume: 211
Issue: 2
Page range: 422-426
Description

This paper studies center conditions and bifurcation of limit cycles from the equator for a class of polynomial differential system of order seven. By converting real planar system into complex system, we established the relation of focal values of a real system with singular point quantities of its concomitant system, and the recursion formula for the computation of singular point quantities of a complex system at the infinity. Therefore, the first 14 singular point quantities of a complex system at the infinity are deduced by using computer algebra system Mathematica. What's more, the conditions for the infinity of the real system to be a center or 14 degree. ne focus are derived, respectively. A system of order seven that bifurcates 12 limit cycles from the infinity is constructed for the first time.
Subjects

*Mathematics
*Unclassified
Keywords

Polynomial system, Seven order, The equator, Focal value, Singular point quantity, Bifurcation of limit cycles