%0 Journal Article %1 murray1982parameter %A Murray, J D %D 1982 %J J Theor Biol %K pattern_formation reaction-diffusion %N 1 %P 143-163 %T Parameter space for Turing instability in reaction diffusion mechanisms: a comparison of models %U http://www.ncbi.nlm.nih.gov/pubmed/7176665 %V 98 %X Several current reaction diffusion mechanisms have been proposed as models for morphogenesis in the Turing (1952) sense. We show that the major differences between them are in the parameter domain for diffusion-driven instability. A simple method is given for computing these domains in the parameter space. The range of parameters for numerical simulation for spatially heterogeneous solutions is then obvious. The size of the domains vary markedly, with the Thomas (1976) system giving the largest among the practical systems. It is premature to say one mechanism is a best model until further experimental information is available on the “morphogens” involved, the order of magnitude of the rate constants and the type of reaction kinetics involved. All of the models discussed exhibit properties consistent with the idea of developmental bifurcations and the punctuated equilibrium theory of macroevolution.

@article{murray1982parameter, abstract = {Several current reaction diffusion mechanisms have been proposed as models for morphogenesis in the Turing (1952) sense. We show that the major differences between them are in the parameter domain for diffusion-driven instability. A simple method is given for computing these domains in the parameter space. The range of parameters for numerical simulation for spatially heterogeneous solutions is then obvious. The size of the domains vary markedly, with the Thomas (1976) system giving the largest among the practical systems. It is premature to say one mechanism is a best model until further experimental information is available on the “morphogens” involved, the order of magnitude of the rate constants and the type of reaction kinetics involved. All of the models discussed exhibit properties consistent with the idea of developmental bifurcations and the punctuated equilibrium theory of macroevolution.}, added-at = {2015-04-13T18:06:07.000+0200}, author = {Murray, J D}, biburl = {https://www.bibsonomy.org/bibtex/2bdd12d328853e970ae5053d7a6f44b9a/peter.ralph}, interhash = {52cd4f61980f20441e5f55bc73b0c6d7}, intrahash = {bdd12d328853e970ae5053d7a6f44b9a}, journal = {J Theor Biol}, keywords = {pattern_formation reaction-diffusion}, month = sep, number = 1, pages = {143-163}, pmid = {7176665}, timestamp = {2015-04-13T18:06:07.000+0200}, title = {Parameter space for {Turing} instability in reaction diffusion mechanisms: a comparison of models}, url = {http://www.ncbi.nlm.nih.gov/pubmed/7176665}, volume = 98, year = 1982 }