
A Note on the Expansion of the First Order Melnikov Function Near a Class of 3polycycle 

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KeyWord:Limit cycle; Quadratic polynomial system; 3polycycle 
Author Name  Affiliation  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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Abstract: 
This paper comments that there exist some mistakes in the asymptotic expansion of the ﬁrst order Menikov function near a 3polycycle given by Theorem 3.1 of [2]. We present a correction to the theorem, and then use it to show that only one limit cycle can be found near a 3polycycle for a class of quadratic systems. 


