Periodic forcing on degenerate Hopf bifurcation
type: Item
instance of: scholarly article
title: Periodic forcing on degenerate Hopf bifurcation
zbMATH Open document ID: 1472.34074
author: Qigang Yuan
author: Jingli Ren
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2021-06-17T00:00:00Z
review text: In this work, the authors deal with the effect of periodic forcing on a system exhibiting a degenerate Hopf bifurcation. Two methods are employed to investigate bifurcations of periodic solution for the periodically forced system. It is obtained by averaging method that the system undergoes fold bifurcation, transcritical bifurcation, and even degenerate Hopf bifurcation of periodic solution. On the other hand, it is also shown by the Poincaré map that the system will undergo fold bifurcation, transcritical bifurcation, Neimark-Sacker bifurcation and flip bifurcation. Finally, we make a comparison between these two methods. The method is novel and enriches the bifurcation theory of delayed differential equation to some degree.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 7360489
zbMATH Keywords: periodic forcing
zbMATH Keywords: degenerate Hopf bifurcation
zbMATH Keywords: averaging method
zbMATH Keywords: Poincaré map
zbMATH Keywords: complexity
reviewed by: Changjin Xu
describes a project that uses: AUTO
describes a project that uses: AUTO-07P
MaRDI profile type: Publication
full work available at URL: dcdsb.2020208
OpenAlex ID: W3040509139
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DOI: 10.3934/DCDSB.2020208
description: scientific article; zbMATH DE number 7360489