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Qualitative Theory of Dynamical Systems

, Volume 18, Issue 3, pp 1077–1112 | Cite as

Bifurcation of Periodic Orbits of a Three-Dimensional Piecewise Smooth System

  • Shenglan Xie
  • Maoan HanEmail author
  • Xuepeng Zhao
Article
  • 67 Downloads

Abstract

We consider a three-dimensional piecewise smooth system having an invariant surface and a closed orbit of multiplicity k on the invariant surface. By using bifurcation techniques and analyzing the number of solutions of bifurcation equations, we study certain bifurcation phenomena near the multiple k closed orbit and obtain some conditions for the existence of periodic orbits bifurcated from it. Moreover, our partial analytical results are demonstrated by some examples.

Keywords

Bifurcation Three-dimensional system Piecewise smooth Closed orbit 

Notes

Acknowledgements

We would like to thank the referees for their valuable suggestions which helped to improve the presentation of the paper.

Compliance with Ethical Standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

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Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China
  2. 2.Department of MathematicsShanghai Normal UniversityShanghaiPeople’s Republic of China
  3. 3.Department of Mathematics and Physics, Nanhu CollegeJiaxing UniversityJiaxingPeople’s Republic of China

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