Turing Bifurcations and Pattern Selection

  • P. Borckmans
  • G. Dewel
  • A. De Wit
  • D. Walgraef
Chapter
Part of the Understanding Chemical Reactivity book series (UCRE, volume 10)

Abstract

Pattern forming instabilities in spatially extended dissipative systems driven away from equilibrium have been the focus of a large activity for many years. The goal of this chapter is to present some theoretical concepts that have been developed to understand and describe these dissipative structures [1] from a macroscopic point of view. Although these methods present generic features we shall only be concerned with chemical patterning and shall not discuss here instabilities in hydrodynamics, liquid crystals and nonlinear optics that all present similar types of organization because the latter have been the subject of recent well-documented reviews [2–5]. Moreover, we essentially consider the self-organization of structures discarding the spatial patterning resulting from boundary conditions.

Keywords

Bifurcation Diagram Linear Stability Analysis Bifurcation Parameter Pattern Selection 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 Science+Business Media Dordrecht 1995

Authors and Affiliations

  • P. Borckmans
    • 1
  • G. Dewel
    • 1
  • A. De Wit
    • 1
  • D. Walgraef
    • 1
  1. 1.Service de Chimie-Physique/Center for Nonlinear Phenomena and Complex Systems, CP 231Université Libre de BruxellesBruxellesBelgium

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