Limit cycles in a switching Liénard system
type: Item
instance of: scholarly article
title: Limit cycles in a switching Liénard system
author: Xiangyu Wang
author: Laigang Guo
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-11-08T00:00:00Z
review text: This paper is concerned with a class of quadratic switching Liénard systems with three switching lines. The authors computed Lyapunov constants to study the center conditions and bifurcation of limit cycles of a singular point \((0,0)\). They offered an algorithm to compute Lyapunov constants. Based on the algorithm, they computed the first four Lyapunov constants to obtain center conditions. Finally, they constructed a perturbed quadratic switching Liénard system according to the center condition and computed the Lyapunov constants to prove the existence of six limit cycles around \((0,0)\). This is a new low bound on the maximal number of small-amplitude limit cycles for the quadratic switching Liénard systems.
reviewed by: Kuilin Wu
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7613232
zbMATH Keywords: Liénard system
zbMATH Keywords: switching lines
zbMATH Keywords: Lyapunov constant
zbMATH Keywords: center
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: dcdsb.2022132
OpenAlex ID: W4285247001
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DOI: 10.3934/DCDSB.2022132
description: scientific article; zbMATH DE number 7613232