Limit cycles in a switching Liénard system

Xiangyu Wang; Laigang Guo

doi:10.3934/dcdsb.2022132

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2023, Volume 28, Issue 2: 1503-1512. Doi: 10.3934/dcdsb.2022132

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Limit cycles in a switching Liénard system

Xiangyu Wang^1, and
Laigang Guo^2, ,

1.
School of Mathematical Sciences, Beihang University, Beijing 100191, China
2.
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems (MOE), Beijing Normal University, Beijing 100875, China

^* Corresponding author: Laigang Guo
^* Corresponding author: Laigang Guo

Received: January 31, 2022

Revised: April 30, 2022

Early access: July 2022

Published: February 2023

The second author is supported by the Fundamental Research Funds for the Central Universities 2021NTST32

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Abstract

In this paper, we consider a class of quadratic switching Liénard systems with three switching lines. We give an algorithm for computing the Lyapunov constants of this system. Based on this method, we obtain a center condition and three limit cycles bifurcating from the focus $ (0,0) $. Further, an example of quadratic switching systems is constructed to show the existence of six limit cycles bifurcating from the center. This is a new low bound on the maximal number of small-amplitude limit cycles obtained in such quadratic switching systems.

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Mathematics Subject Classification: Primary: 34C05, 34C07.

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