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A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones |
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| Authors: | Shimin Li Hebai Chen Ting Chen Kuilin Wu |
| Institution: | School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong 510320, China;School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China; School of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China |
| 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}. |
| Keywords: | Bendixson-Dulac theorem Refracted system Limit cycle |
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