Critical timescales and time intervals for coupled linear processes

Simpson, Matthew, Ellery, Adam, McCue, Scott W., & Baker, Ruth (2013) Critical timescales and time intervals for coupled linear processes. ANZIAM Journal, 54(3), pp. 127-142.

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In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

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3 citations in Scopus
3 citations in Web of Science®
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ID Code: 56374
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: mathematical modelling, reaction diffusion equation, coupled reaction diffusion equation, mean action time, critical time
DOI: 10.1017/S1446181113000059
ISSN: 1446-8735
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Australian Mathematical Society
Copyright Statement: This is the author's version of an article that was accepted for publication and appears in a revised form, subsequent to peer review and/or editorial input, in the ANZIAM Journal, (Volume 54, Issue 03 [January 2013]), pp 127-142.
Deposited On: 11 Jan 2013 01:56
Last Modified: 30 Oct 2013 11:17

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