A skeleton structure of self-replicating dynamics
type: Item
instance of: scholarly article
title: A skeleton structure of self-replicating dynamics
zbMATH Open document ID: 0936.35090
DOI: 10.1016/S0167-2789(99)00010-X
author: Yasumasa Nishiura
author: Daishin Ueyama
published in: Physica D
publication date: 2000-05-11T00:00:00Z
review text: The aim of this paper is to present a key mechanism for the self-replicating dynamics for a class of model systems including the Gray-Scott model. As a model which shows self-replicating patterns of propagating type it is considered the system: \[ \partial u/\partial t=D_u\nabla^2u+ u(u-v^2-\alpha),\;\partial v/\partial t=D_v\nabla^2 v+mu-v, \] where \(u\) and \(v\) are concentrations of the chemical materials \(U\) and \(V\), respectively; \(D_u,D_v\) are diffusion coefficients, \(\alpha\) and \(m\) are non-negative parameters. This system is considered on a finite interval subject to Neumann (zero flux) boundary condition. The length of interval and \(\alpha\) are control parameters. The paper contains results concerning the behaviour of solutions. There are three different phases of dynamics of self-replicating patterns: 1. Steady or traveling (an isolated pulse-like pattern stays or travels almost without changing its shape). 2. Splitting phase (some of the pulses split into two parts). 3. Convergence to a final state.
reviewed by: Ion Onciulescu
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1370187
zbMATH Keywords: Gray-Scott model
zbMATH Keywords: pulse-like pattern
describes a project that uses: HomCont
describes a project that uses: AUTO
MaRDI profile type: Publication
cites work: WAVE-SPLITTING IN THE BISTABLE GRAY-SCOTT MODEL
cites work: Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
cites work: EXPERIMENTAL STUDY OF STATIONARY TURING PATTERNS AND THEIR INTERACTION WITH TRAVELING WAVES IN A CHEMICAL SYSTEM
cites work: Pattern formation in the one-dimensional Gray - Scott model
cites work: Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach
cites work: Q3841910
cites work: Dynamics of self-replicating patterns in the one-dimensional Gray-Scott model
full work available at URL: s0167-2789(99)00010-x
OpenAlex ID: W2076644075
description: scientific article; zbMATH DE number 1370187