Homoclinic bifurcations at the onset of pulse self-replication
type: Item
instance of: scholarly article
title: Homoclinic bifurcations at the onset of pulse self-replication
zbMATH Open document ID: 1217.34074
published in: Journal of Differential Equations
publication date: 2007-01-16T00:00:00Z
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5116263
zbMATH Keywords: symmetric homoclinic orbits
zbMATH Keywords: multi-pulse orbits
zbMATH Keywords: homoclinic bifurcations
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: autocatalysis
zbMATH Keywords: self-replicating pulses
author: Arjen Doelman
author: Tasso J. Kaper
author: Lambertus A. Peletier
describes a project that uses: XPPAUT
MaRDI profile type: Publication
full work available at URL: j.jde.2006.03.026
OpenAlex ID: W2136303057
cites work: Q3331506
cites work: The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form travelling waves
cites work: The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. II. An initial-value problem with an immobilized or nearly immobilized autocatalyst
cites work: The Gierer \(\&\) Meinhardt system: The breaking of homoclinics and multi-bump ground states
cites work: Slowly modulated two-pulse solutions in the Gray--Scott model. II: Geometric theory, bifurcations, and splitting dynamics
cites work: Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach
cites work: Large stable pulse solutions in reaction-diffusion equations
cites work: A stability index analysis of 1-D patterns of the Gray-Scott model
cites work: Homoclinic explosions and implosions
cites work: Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations
cites work: Pattern formation in the one-dimensional Gray - Scott model
cites work: Homoclinic Stripe Patterns
cites work: \(2^n\)-splitting or edge-splitting? A manner of splitting in dissipative systems
cites work: Simulating, Analyzing, and Animating Dynamical Systems
cites work: Q5658861
cites work: Geometric singular perturbation theory for ordinary differential equations
cites work: Q5110819
cites work: Stability and instability in the Gray-Scott model: The case of equal diffusivities
cites work: Exact Homoclinic and Heteroclinic Solutions of the Gray--Scott Model for Autocatalysis
cites work: Invariant manifolds
cites work: The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
cites work: A Geometric Proof of the Kwong-McLeod Uniqueness Result
cites work: The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime
cites work: Pulse‐Splitting for Some Reaction‐Diffusion Systems in One‐Space Dimension
cites work: The existence and stability of spike equilibria in the one-dimensional Gray -- Scott model on a finite domain
cites work: The Existence and Stability of Spike Equilibria in the One‐Dimensional Gray–Scott Model: The Low Feed‐Rate Regime
cites work: Elements of applied bifurcation theory
cites work: Static spike autosolitons in the Gray-Scott model.
cites work: Stability of the Static Spike Autosolitons in the Gray--Scott Model
cites work: Q4221182
cites work: A skeleton structure of self-replicating dynamics
cites work: Q3127440
cites work: Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
cites work: Invariant manifolds in singular perturbation problems for ordinary differential equations
cites work: Dynamics of self-replicating patterns in the one-dimensional Gray-Scott model
DOI: 10.1016/J.JDE.2006.03.026
description: scientific article; zbMATH DE number 5116263