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Chemical and Biological Applications of Turing Systems

  • Vicenç Méndez
  • Sergei Fedotov
  • Werner Horsthemke
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Turing’s paper on diffusion-driven instabilities in nonequilibrium reaction–diffusion systems as a means of biological pattern formation [440] 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 [26]. 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.

Keywords

Hopf Bifurcation Turing Pattern Turing System Turing Instability Uniform Steady State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vicenç Méndez
    • 1
  • Sergei Fedotov
    • 2
  • Werner Horsthemke
    • 3
  1. 1.Dept. de Física Grup de Física EstadísticaUniversitat Autònoma de BarcelonaBellaterra Edifici CcSpain
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK
  3. 3.Department of ChemistrySouthern Methodist UniversityDallasUSA

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