Center Conditions and Bifurcation of Limit Cycles at Nilpotent Critical Point in a Quintic Lyapunov System
Received:May 09, 2010  Revised:November 20, 2010
Key Word: three-order nilpotent critical point   center-focus problem   bifurcation of limit cycles   quasi-Lyapunov constant.  
Fund ProjectL:Supported by the Natural Science Foundation of Shandong Province (Grant No.Y2007A17).
Author NameAffiliation
Feng LI School of Science, Linyi University, Shandong 276005, P. R. China 
Yin Lai JIN School of Science, Linyi University, Shandong 276005, P. R. China 
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      In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.
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