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Localized Turing and Turing-Hopf Patterns

  • P. Borckmans
  • O. Jensen
  • V. O. Pannbacker
  • E. Mosekilde
  • G. Dewel
  • A. De Wit
Part of the Springer Series in Synergetics book series (SSSYN, volume 65)

Abstract

In systems driven away from thermodynamic equilibrium, patchiness often arises through the occurrence of symmetry breaking bifurcations. Diffusive instabilities resulting from differential diffusion processes acting in the presence of some autocatalytic kinetic scheme enter that class of phenomena to produce stationary space periodic (Turing) or spatiotemporal (Hopf) patterns. Turing patterns have at last recently been obtained when the isothermal Chlorite-Iodide-Malonic Acid (CIMA) reaction takes place in a continuously fed gel reactor in the presence of starch. On varying the malonic acid or starch concentrations a transition from stationary Turing structures to Hopf wavy patterns occurs. In the transition region, where both instabilities interact, a host of interesting behaviours may occur. Among these, new intrinsically localized patterns may form that give rise to new types of patchinesses. All of these structures may be accounted for through the study of the bifurcation behaviour of simple theoretical reaction-diffusion models.

Keywords

Hopf Bifurcation Bifurcation Diagram Malonic Acid Bifurcation Parameter Amplitude Equation 
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 1995

Authors and Affiliations

  • P. Borckmans
  • O. Jensen
  • V. O. Pannbacker
  • E. Mosekilde
  • G. Dewel
  • A. De Wit

There are no affiliations available

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