Resonant parametric perturbations of the Hopf bifurcation
type: Item
instance of: scholarly article
title: Resonant parametric perturbations of the Hopf bifurcation
zbMATH Open document ID: 0588.34031
DOI: 10.1016/0022-247X(86)90035-1
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The effects of periodic parametric perturbations on a system undergoing Hopf bifurcation are studied in detail. Of primary interest is the case of resonance between the Hopf bifurcation frequency and the perturbation frequency. The method of alternative problems is used to obtain the small nonlinear periodic solutions. It is shown that for a certain range of parameters, the Hopf solution is modified to give rise to jump response as well as isolated solutions. For some parameter combinations, stable solutions can get unstable and may bifurcate into aperiodic or amplitude modulated motions.
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 3944327
zbMATH Keywords: first order differential equation
zbMATH Keywords: periodic parametric perturbations
zbMATH Keywords: resonance
zbMATH Keywords: Hopf bifurcation
author: A. K. Bajaj
MaRDI profile type: Publication
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full work available at URL: 0022-247x(86)90035-1
OpenAlex ID: W2072535538
description: scientific article; zbMATH DE number 3944327