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

@article{citeulike:2970377, 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.}, address = {Department of Human Anatomy and Genetics University of Oxford, UK. miura-takashi@umin.ac.jp}, author = {Miura, T. and Maini, P. K. }, citeulike-article-id = {2970377}, issn = {1447-6959}, journal = {Anatomical science international / Japanese Association of Anatomists}, keywords = {reaction-diffusion}, month = {September}, number = {3}, pages = {112--123}, posted-at = {2008-07-07 16:12:25}, priority = {4}, title = {Periodic pattern formation in reaction-diffusion systems: an introduction for numerical simulation.}, url = {http://view.ncbi.nlm.nih.gov/pubmed/15453612}, volume = {79}, year = {2004} }

TY - JOUR ID - citeulike:2970377 L3 - citeulike-article-id:2970377 TI - Periodic pattern formation in reaction-diffusion systems: an introduction for numerical simulation. JF - Anatomical science international / Japanese Association of Anatomists VL - 79 IS - 3 SP - 112 EP - 123 AD - Department of Human Anatomy and Genetics University of Oxford, UK. miura-takashi@umin.ac.jp SN - 1447-6959 N2 - 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. KW - reaction-diffusion AU - Miura, T AU - Maini, PK PY - 2004/09// UR - http://view.ncbi.nlm.nih.gov/pubmed/15453612 ER -