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A Note on the Expansion of the First Order Melnikov Function Near a Class of 3-polycycles
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KeyWord:Limit cycle  Quadratic polynomial system  3-polycycle
Author NameAffiliation
Yanqin Xiong School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China 
Maoan Han Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China 
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      This paper comments that there exist some mistakes in the asymptotic expansion of the first order Menikov function near a 3-polycycle given by Theorem 3.1 of \cite{h3a1}. We present a correction to the theorem, and then use it to show that only one limit cycle can be found near a 3-polycycle for a class of quadratic systems.