The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime
type: Item
instance of: scholarly article
title: The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime
zbMATH Open document ID: 1136.35003
author: Theodore Kolokolnikov
author: Michael J. Ward
author: Juncheng Wei
published in: Physica D
publication date: 2005-06-01T00:00:00Z
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 2173562
zbMATH Keywords: saddle-node bifurcation
zbMATH Keywords: multi-bump solution
zbMATH Keywords: drift instability
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: matched asymptotic expansions
zbMATH Keywords: combination of asymptotic and numerical methods
describes a project that uses: LAPACK
describes a project that uses: nag
describes a project that uses: d03pcf
describes a project that uses: NAG
describes a project that uses: COLSYS
MaRDI profile type: Publication
full work available at URL: j.physd.2005.02.009
OpenAlex ID: W2022523204
cites work: Q4841244
cites work: A Collocation Solver for Mixed Order Systems of Boundary Value Problems
cites work: Reaction-diffusion models for biological pattern formation
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. I: Asymptotic construction and stability
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: A stability index analysis of 1-D patterns of the Gray-Scott model
cites work: Pattern formation in the one-dimensional Gray - Scott model
cites work: \(2^n\)-splitting or edge-splitting? A manner of splitting in dissipative systems
cites work: The motion of weakly interacting pulses in reaction-diffusion systems
cites work: Q4345268
cites work: Q5110819
cites work: Dynamical Hysteresis without Static Hysteresis: Scaling Laws and Asymptotic Expansions
cites work: Pattern Selection for Two Breathers
cites work: The Dynamics of Multispike Solutions to the One-Dimensional Gierer--Meinhardt Model
cites work: The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
cites work: The Existence and Stability of Spike Equilibria in the One‐Dimensional Gray–Scott Model: The Low Feed‐Rate Regime
cites work: Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model
cites work: Zigzag and Breakup Instabilities of Stripes and Rings in the Two‐Dimensional Gray–Scott Model
cites work: On ring-like solutions for the Gray–Scott model: existence, instability and self-replicating rings
cites work: Layer Oscillations in Reaction-Diffusion Systems
cites work: Axisymmetric ring solutions of the 2D Gray-Scott model and their destabilization into spots
cites work: Traveling spike autosolitons in the Gray-Scott model
cites work: Stability of the Static Spike Autosolitons in the Gray--Scott Model
cites work: Static spike autosolitons in the Gray-Scott model.
cites work: Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations
cites work: Global bifurcational approach to the onset of spatio-temporal chaos in reaction diffusion systems
cites work: A skeleton structure of self-replicating dynamics
cites work: Spatio-temporal chaos for the Gray-Scott model
cites work: Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
cites work: The Slow Dynamics of Two-Spike Solutions for the Gray--Scott and Gierer--Meinhardt Systems: Competition and Oscillatory Instabilities
cites work: Numerical Challenges for Resolving Spike Dynamics for Two One-Dimensional Reaction-Diffusion Systems
cites work: Dynamics of self-replicating patterns in the one-dimensional Gray-Scott model
DOI: 10.1016/J.PHYSD.2005.02.009
description: scientific article; zbMATH DE number 2173562