Homoclinic orbits in a simple chemical model of an autocatalytic reaction
type: Item
instance of: scholarly article
title: Homoclinic orbits in a simple chemical model of an autocatalytic reaction
zbMATH Open document ID: 0659.34044
DOI: 10.1016/0167-2789(88)90069-3
author: Christian Kaas-Petersen
author: Stephen K. Scott
published in: Physica D
publication date: 1988-01-01T00:00:00Z
review text: In a one-parameter family of ODEs a periodic solution may disappear via the formation of a homoclinic orbit as the parameter c, say, passes through a critical value \(c^*\). The period of the solution becomes infinite, growing as \(\ln | c-c^*|\) as \(c\to c^*\) when the stationary solution at which the homoclinic orbit begins and ends is hyperbolic. If the stationary solution is non-hyperbolic, i.e. a bifurcation point, then the period tends to infinity more quickly than this logarithmic form, growing as \((| c-c^*|)^{-1/2}\). We show that although bifurcation point and homoclinic orbit formation are both codimension-1 phenomena, a homoclinic orbit related to a non- hyperbolic stationary solution is essentially a codimension-1 situation. Both types of homoclinic orbit have been found in a simple model for an autocatalytic chemical reaction scheme.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 4077759
zbMATH Keywords: stationary solution
zbMATH Keywords: bifurcation point
zbMATH Keywords: autocatalytic chemical reaction scheme
describes a project that uses: AUTO
describes a project that uses: AUTO-86
MaRDI profile type: Publication
full work available at URL: 0167-2789(88)90069-3
OpenAlex ID: W1993686135
cites work: Local and global behavior near homoclinic orbits
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Q4161604
cites work: Q3930015
cites work: The Saddle-Node Separatrix-Loop Bifurcation
cites work: The Lorenz equations: bifurcations, chaos, and strange attractors
cites work: Towards a classification of generic bifurcations in dissipative dynamical systems
description: scientific article; zbMATH DE number 4077759