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The Number of Limit Cycles in a Class of Piecewise Polynomial Systems
  
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KeyWord:Piecewise smooth system; Melnikov function; ECT-system; Limit cycle
Author NameAffiliation
Shanshan Liu Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Xuyi Jin Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Yujie Xiong Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
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Abstract:
      In this paper, we pay attention to the number of limit cycles for a class of piecewise smooth near-Hamiltonian systems. By using the expression of the first order Melnikov function and some known results about Chebyshev systems, we study upper bound of the number of limit cycles in Hopf bifurcation and Poincar\'{e} bifurcation respectively.