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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 Name | Affiliation | | 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}. |
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