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Numerical Bifurcation Analysis of a 3D Turing-type Reaction-Diffusion Model

Song, Weiyan and Wubs, Fred W. and Thies, Jonas and Baars, Sven (2018) Numerical Bifurcation Analysis of a 3D Turing-type Reaction-Diffusion Model. Communications in Nonlinear Science and Numerical Simulation, 60, pp. 145-164. Elsevier. DOI: 10.1016/j.cnsns.2018.01.003 ISSN 1007-5704

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Official URL: https://doi.org/10.1016/j.cnsns.2018.01.003

Abstract

We perform a numerical study of a two-component reaction-diffusion model. By using numerical continuation methods, combined with state-of-the-art sparse linear and eigenvalue solvers, we systematically compute steady state solutions and analyze their stability and relations in both two and three space dimensions. The approach gives a more reliable and complete picture than previous efforts based on time integration schemes and is also typically much more efficient in terms of computing time. We are therefore able to produce a rich bifurcation diagram showing a variety of solution patterns and transitions.

Item URL in elib:https://elib.dlr.de/114767/
Document Type:Article
Title:Numerical Bifurcation Analysis of a 3D Turing-type Reaction-Diffusion Model
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Song, Weiyanweiyan.aibao (at) gmail.comUNSPECIFIED
Wubs, Fred W.f.w.wubs (at) rug.nlUNSPECIFIED
Thies, JonasJonas.Thies (at) dlr.deUNSPECIFIED
Baars, Svens.baars (at) rug.nlUNSPECIFIED
Date:July 2018
Journal or Publication Title:Communications in Nonlinear Science and Numerical Simulation
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:60
DOI :10.1016/j.cnsns.2018.01.003
Page Range:pp. 145-164
Editors:
EditorsEmail
Chandre, C.UNSPECIFIED
Publisher:Elsevier
ISSN:1007-5704
Status:Published
Keywords:continuation; pattern formation; bifurcation diagram; stability
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > High Performance Computing
Institut of Simulation and Software Technology
Deposited By: Thies, Jonas
Deposited On:12 Jan 2018 11:23
Last Modified:07 May 2018 08:50

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  • Numerical Bifurcation Analysis of a 3D Turing-type Reaction-Diffusion Model. (deposited 12 Jan 2018 11:23) [Currently Displayed]

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