The Mathematical Institute, University of Oxford, Eprints Archive

Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation

Miura, T. and Maini, P. K. (2004) Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation. Anatomical Science International, 79 (3). pp. 112-123.

[img]
Preview
PDF
425Kb

Abstract

The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology.

Item Type:Article
Uncontrolled Keywords:mathematical modeling, numerical simulation,pattern formation, Turing
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:359
Deposited By:Philip Maini
Deposited On:13 Nov 2006
Last Modified:20 Jul 2009 14:20

Repository Staff Only: item control page