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Synergetics pp 18-21 | Cite as

Bifurcation Diagram of Model Chemical Reactions

  • M. Kaufman-Herschkowitz
  • T. Erneux
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 3)

Abstract

Some general principles underlying pattern formation and the onset of temporal oscillations in reaction/diffusion systems can be derived from the detailed bifurcation analysis of nonlinear differential equations of the form:
$$\begin{array}{l} \frac{\partial }{{{\partial _t}}}{X_i} = {F_i}({X_i},{X_i},...{X_n};\lambda ) + {D_i}\Delta {X_i} \\ 1 \le i \le n \\ \end{array}$$
Fi is a nonlinear rate function of the concentrations Xj where λ represents a set of characteristic physico-chemical parameters. The second term is Fick’s linear law for diffusion.

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References

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    Erneux, T. and Herschkowitz-Kaufman, M., submitted for publication.Google Scholar
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    Erneux, T. and Herschkowitz-Kaufman, M.: J. Chem. Phys., 66, 248–250 (1977)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • M. Kaufman-Herschkowitz
  • T. Erneux

There are no affiliations available

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