# American Institute of Mathematical Sciences

March  2021, 26(3): 1565-1577. doi: 10.3934/dcdsb.2020173

## The Poincaré bifurcation of a SD oscillator

 1 School of Mathematics, Soochow University, 215006, Suzhou, China 2 School of Mathematics (Zhuhai), Sun Yat-sen University, 519082, Zhuhai, China

* Corresponding author

Received  November 2019 Revised  January 2020 Published  May 2020

A van der Pol damped SD oscillator, which was proposed by Ruilan Tian, Qingjie Cao and Shaopu Yang (2010, Nonlinear Dynamics, 59, 19-27), is studied. By improving the criterion function of determining the lowest upper bound of the number of zeros of Abelian Integrals, we show that the number of zeros of Abelian integrals of this SD oscillator is two which is sharp.

Citation: Yangjian Sun, Changjian Liu. The Poincaré bifurcation of a SD oscillator. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1565-1577. doi: 10.3934/dcdsb.2020173
##### References:

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##### References:
The global phase portraits of system (1.6) for $0<a<1$ and $\epsilon = 0$
The phase portraits of system (2.1)
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