Bifurcation of limit cycles in a family of piecewise smooth systems via averaging theory

Shanshan Liu; Maoan Han

doi:10.3934/dcdss.2020133

Article Contents

2020, Volume 13, Issue 11: 3115-3124. Doi: 10.3934/dcdss.2020133

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Bifurcation of limit cycles in a family of piecewise smooth systems via averaging theory

Shanshan Liu^1, and
Maoan Han^1,2, ,

1.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

^* Corresponding author: Maoan Han
^* Corresponding author: Maoan Han

Received: November 30, 2018

Revised: January 31, 2019

Early access: November 2019

Published: July 2020

The second author is supported by National Natural Science Foundation of China (11771296 and 11431008)

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Abstract

In this paper we study the maximal number of limit cycles for a class of piecewise smooth near-Hamiltonian systems under polynomial perturbations. Using the second order averaging method, we obtain the maximal number of limit cycles of two systems respectively. We also present an application.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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