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Bifurcation of limit cycles at the equator

Qi Zhang
Zhao Zhengquan
Gui Weihua
Journal / Anthology

Year: 2009
Volume: 211
Issue: 2
Page range: 422-426

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.


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