Data for paper "Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems"

Name: Data for paper "Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems"
Published: 2018-01-01T00:00:00Z
License: https://ora.ox.ac.uk/terms_of_use

Krause, A; Gaffney, E

Documentation:: All data were created using Comsol as described in the paper. The .csv files can be loaded and plotted via Matlab, and the .m files should function as runnable scripts. Each Figure has its own folder containing data sufficient to reproduce the Figure.

Actions

Email

Email this record

Send the bibliographic details of this record to your email address.

Your Email
Please enter the email address that the record information will be sent to.

-
Your message (optional)
Please add any additional information to be included within the email.
Cite

Cite this record

APA Style

Krause, A., & Gaffney, E. (2018). Data for paper "Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems". University of Oxford.

MLA Style

Krause, A., and E. Gaffney. Data for Paper "Heterogeneity Induces Spatiotemporal Oscillations in Reaction-Diffusion Systems". University of Oxford, 2018.

Chicago Style

Krause, A, and E Gaffney. 2018. “Data for Paper ‘Heterogeneity Induces Spatiotemporal Oscillations in Reaction-Diffusion Systems.’” University of Oxford.
Share
Print

Access Document

Files:: FigureData.zip

(zip, 553.3MB, Terms of use)

Authors/Creators

+ Krause, A More by this author/creator

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Creator

+ Gaffney, E More by this author/creator

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Creator, Creator, Creator, Principal Investigator (PI)

+ Biotechnology and Biological Sciences Research Council More from this funder

Funder identifier:: https://ror.org/00cwqg982
Grant:: BB/N006097/1

Publisher:: University of Oxford
Publication date:: 2018
DOI:: 10.5287/bodleian:QoDzZP7Dz

Language:: English
Pubs id:: 1479984
UUID:: uuid:200d97c9-6d70-4b12-866c-85465d7a079e
Local pid:: pubs:1479984
Deposit date:: 2018-04-29

Related item:: Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
Description:: We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well-known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity.

Terms of use

Licence:: Terms and Conditions of Use for Oxford University Research Archive

Views and Downloads

About views and downloads

If you are the owner of this record, you can report an update to it here: Report update to this record

Dataset

Data for paper "Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems"

Actions

Access Document

Authors/Creators

Terms of use

Views and Downloads

Altmetrics

Dimensions

Dataset

Data for paper "Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems"

Actions

Access Document

Authors/Creators

Funding

Bibliographic Details

Item Description

Related Items

Terms of use

Metrics

Views and Downloads

Altmetrics

Dimensions