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Volume 3, Issue 2
A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones

Shimin Li, Hebai Chen, Ting Chen & Kuilin Wu

DOI: 10.12150/jnma.2021.275

J. Nonl. Mod. Anal., 3 (2021), pp. 275-281.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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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 [16].

  • Keywords

Bendixson-Dulac theorem, Refracted system, Limit cycle.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JNMA-3-275, author = {Li , ShiminChen , HebaiChen , Ting and Wu , Kuilin}, title = {A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {3}, number = {2}, pages = {275--281}, 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 [16].

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2021.275}, url = {http://global-sci.org/intro/article_detail/jnma/18790.html} }
TY - JOUR T1 - A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones AU - Li , Shimin AU - Chen , Hebai AU - Chen , Ting AU - Wu , Kuilin JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 275 EP - 281 PY - 2021 DA - 2021/04 SN - 3 DO - http://doi.org/10.12150/jnma.2021.275 UR - https://global-sci.org/intro/article_detail/jnma/18790.html KW - Bendixson-Dulac theorem, Refracted system, Limit cycle. AB -

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 [16].

Li , ShiminChen , HebaiChen , Ting and Wu , Kuilin. (2021). A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones. Journal of Nonlinear Modeling and Analysis. 3 (2). 275-281. doi:10.12150/jnma.2021.275
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