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Limit Cycles for a Discontinuous Quintic Polynomial Differential System

  • Bo HuangEmail author
Article

Abstract

In this article, we study the maximum number of limit cycles for a discontinuous quintic differential system. Using the first-order averaging method, we explain how limit cycles can bifurcate from the period annulus around the center of the considered system when it is perturbed inside a class of discontinuous quintic polynomial differential systems. Our results show that the lower bound and the upper bound of the number of limit cycles, 8 and 10 respectively, that can bifurcate from the period annulus around the center.

Keywords

Averaging method Center Discontinuous quintic system Limit cycle Period annulus 

Mathematics Subject Classification

34C05 34C07 

Notes

Acknowledgements

I wish to thank Xiuli Cen for her helpful suggestions and to Dongming Wang for his profound concern and encouragement. I also wish to thank the reviewers for their valuable comments that have helped to improve the presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LMIB-School of Mathematics and Systems ScienceBeihang UniversityBeijingPeople’s Republic of China
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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