Chemical and Biological Applications of Turing Systems
Turing’s paper on diffusion-driven instabilities in nonequilibrium reaction–diffusion systems as a means of biological pattern formation  attracted little attention for about two decades, as shown by the citation histogram in Fig. 12.1. One of the first scientists to be intrigued by Turing’s ideas was Wardlaw, a botanist who thought about ways to test the mechanism experimentally [468, 470, 469]. By the early 1970s theoretical biologists and biomathematicians began to explore in earnest if Turing instabilities could explain spatial pattern formation in a variety of living systems and a considerable body of theoretical work was produced, see for example [157, 279, 231, 239, 182, 183, 264, 261, 308]. Morphogen-based pattern formation, where the long-range influence of signaling molecules induces structure, is a well-established phenomenon in developmental biology . However, definitive evidence for a Turing mechanism of pattern formation within a morphogen system is still lacking. Several promising candidate systems exist and are discussed in Sect. 12.2.
KeywordsHopf Bifurcation Turing Pattern Turing System Turing Instability Uniform Steady State
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