Propagating Waves and Target Patterns in Chemical Systems

  • P. C. Fife
Part of the Springer Series in Synergetics book series (SSSYN, volume 6)


The discovery of propagating waves of various types in chemical reagents has provoked a great deal of research, during the last ten years, into the phenomenology and the underlying mechanisms for such wavelike activity. The research has been performed by natural scientists and mathematicians alike. Most of it has been experimental, but much computer simulation and mathematical analysis has also been done. Chemical wave activity is believed to be prevalent in biological organisms, but the most readily accessible reagent for laboratory study is that discovered by Belousov and Žabotinskiĭ. This mixture has oscillatory or excitable kinetics, depending on the concentrations of the various chemicals in the solution. Both of these regimes have at least two natural time scales: During one period of an oscillation or during one excited “excursion”, most of the variation in the concentration of the reactants occurs within a brief interval of time. The time scale associated with this brief spurt of activity is much shorter than that associated with the slow variation which occurs before and after. This is well known from experiment and computation, and is evident from scaling analyses of model kinetic equations performed in [1] and elsewhere. Spatial structures are also prevalent in unstirred layers of this reagent ([23]; [2], [22], [24], and references therein). Target patterns (expanding concentric circular waves) are among the most prevalent of these structures. Here again, disparate space and time scales are evident from computer simulation of propagating waves [3].


Wave Front Wave Train Excitable Medium Relaxation Oscillator Target Pattern 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • P. C. Fife
    • 1
  1. 1.Mathematics DepartmentUniversity of ArizonaTucsonUSA

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