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

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

* Corresponding author: Maoan Han

Received  December 2018 Revised  February 2019 Published  November 2019

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

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.

Citation: Shanshan Liu, Maoan Han. Bifurcation of limit cycles in a family of piecewise smooth systems via averaging theory. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020133
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