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A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones
  
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KeyWord:Bendixson-Dulac theorem; Refracted system; Limit cycle
Author NameAffiliation
Shimin Li School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong 510320, China 
Hebai Chen School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China 
Ting Chen School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong 510320, China 
Kuilin Wu School of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China 
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Abstract:
      This note extends the Bendixson-Dulac theorem to refracted systems with multiple zones. As an application, we prove that piecewise linear Duffing-type system has neither crossing limit cycles nor sliding limit cycles Therefore, it gives a positive answer to the Conjecture of \cite{TA2007}.