A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones

Authors

  • Shimin Li
  • Hebai Chen School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China 
  • Ting Chen
  • Kuilin Wu School of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China 

DOI:

https://doi.org/10.12150/jnma.2021.275

Keywords:

Bendixson-Dulac theorem, Refracted system, Limit cycle.

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].

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Published

2024-04-10

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Issue

Vol. 3 No. 2 (2021)

Section

Articles

How to Cite

A Note on the Bendixson-Dulac Theorem for Refracted Systems with Multiple Zones. (2024). Journal of Nonlinear Modeling and Analysis, 3(2), 275-281. https://doi.org/10.12150/jnma.2021.275