On infinite period bifurcations with an application to roll waves
type: Item
instance of: scholarly article
title: On infinite period bifurcations with an application to roll waves
zbMATH Open document ID: 0588.76024
DOI: 10.1007/BF01302938
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: By considering a model equation we are able to derive conditions under which a limit cycle, created (at small amplitude) by a Hopf bifurcation, can be destroyed (at finite amplitude) by an infinite period bifurcation, this latter appearing out of a homoclinic orbit formed by the separatrices of a saddle point equilibrium state. Further, we are able to extend the methods used for showing the existence of an infinite period bifurcation to calculate the amplitude of the limit cycle over its whole range of existence. These ideas are then applied to an equation arising in the theory of roll waves down an open inclined channel, extending previous work to include the case when the Reynolds number is large with the Froude number close to its critical value for the temporal instability of the uniform flow. Here the governing equation reduced to one similar in form to the model equation.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 3945629
zbMATH Keywords: system of first order ordinary differential equations
zbMATH Keywords: limit cycle
zbMATH Keywords: small amplitude
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: destroyed
zbMATH Keywords: finite amplitude
zbMATH Keywords: infinite period bifurcation
zbMATH Keywords: homoclinic orbit
zbMATH Keywords: separatrices of a saddle point equilibrium state
zbMATH Keywords: roll waves
zbMATH Keywords: open inclined channel
zbMATH Keywords: Reynolds number is large
zbMATH Keywords: Froude number close to its critical value
zbMATH Keywords: temporal instability
zbMATH Keywords: uniform flow
author: J. H. Merkin
author: David J. Needham
MaRDI profile type: Publication
cites work: Infinite Period Bifurcation and Global Bifurcation Branches
cites work: On roll waves down an open inclined channel
cites work: An infinite period bifurcation arising in roll waves down an open inclined channel
cites work: Q3207313
cites work: Q3895284
cites work: Q3683220
full work available at URL: https://doi.org/10.1007/bf01302938
OpenAlex ID: W1995234311
description: scientific article; zbMATH DE number 3945629