The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE
type: Item
instance of: scholarly article
title: The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE
zbMATH Open document ID: 0893.34027
DOI: 10.1016/S0167-2789(96)00187-X
author: Ralf W. Wittenberg
author: Philip Holmes
published in: Physica D
publication date: 1997-02-05T00:00:00Z
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 976585
zbMATH Keywords: degenerate local bifurcations
zbMATH Keywords: dynamics
zbMATH Keywords: Brusselator partial differential equations
zbMATH Keywords: normal forms
zbMATH Keywords: spatio-temporal complexity
zbMATH Keywords: chaos
zbMATH Keywords: Šil'nikov chaos
describes a project that uses: AUTO
MaRDI profile type: Publication
cites work: Imperfection sensitivity of interacting Hopf and steady-state bifurcations and their classification
cites work: Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold
cites work: Q4040102
cites work: Q3995227
cites work: Bifurcation analysis of nonlinear reaction diffusion equations I. Evolution equations and the steady state solutions
cites work: Bifurcation analysis of reaction-diffusion equations. III: Chemical oscillations
cites work: Uniqueness and non-uniqueness of normal forms for vector fields
cites work: Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension
cites work: Q3994902
cites work: Applications of centre manifold theory
cites work: Abelian integrals and bifurcation theory
cites work: Computation of normal forms
cites work: Uniqueness of periodic orbits of some vector fields with codimension two singularities
cites work: Q4305607
cites work: Normal forms for nonlinear vector fields. I. Theory and algorithm
cites work: Normal forms for nonlinear vector fields. II. Applications
cites work: A simple global characterization for normal forms of singular vector fields
cites work: Freedom in minimal normal forms
cites work: Local birth of homoclinic chaos
cites work: Local and global behavior near homoclinic orbits
cites work: Singularities and groups in bifurcation theory. Volume II
cites work: Q3940514
cites work: Multiple Bifurcation Problems of Codimension Two
cites work: Multiple bifurcation problems for chemical reactors
cites work: Q4304279
cites work: Q4743116
cites work: Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions
cites work: A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
cites work: Bifurcations of the forced van der Pol oscillator
cites work: Secondary Bifurcation in Nonlinear Diffusion Reaction Equations
cites work: Merging of resonance tongues
cites work: Periodic and Steady-State Mode Interactions Lead to Tori
cites work: Pattern Generation in Space and Aspect
cites work: Q1233671
cites work: Q3994920
cites work: Q4138569
cites work: Perturbation methods, bifurcation theory and computer algebra
cites work: Bifurcation analysis near a double eigenvalue of a model chemical reaction
cites work: Bifurcation to Quasi-Periodic Tori in the Interaction of Steady State and Hopf Bifurcations
cites work: Q5509205
cites work: A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
cites work: Sequence of bifurcations in a three-dimensional system near a critical point
cites work: Singularities of vector fields
cites work: Q4058507
cites work: The chemical basis of morphogenesis
cites work: Normal forms for singularities of vector fields
cites work: A note on: Abelian integrals and bifurcation theory
cites work: ON THE VERSALITY OF A FAMILY OF SYMMETRIC VECTOR FIELDS IN THE PLANE
description: scientific article; zbMATH DE number 976585