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Hopf Cyclicity of a Class of Li\'{e}nard-Type Systems
  
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KeyWord:Hopf cyclicity, polynomial and rational polynomial Li\'{e}nard systems, smooth and piecewise smooth systems
Author NameAffiliation
Hongwei Shi School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, Guangdong 519082, China 
Changjian Liu School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, Guangdong 519082, China 
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Abstract:
      The Hopf cyclicities of some smooth polynomial, rational polynomial and piecewise smooth Li\'{e}nard systems are studied. For two Li\'{e}nard systems with the same damping term and different restoring (or potential) terms, we provide sufficient conditions that the two systems have the same Hopf cyclicity. Then, some examples are given to illustrate the efficiency and applicability of our results.