Synergetics pp 263-291 | Cite as

Chemical and Biochemical Systems

  • Hermann Haken
Part of the Springer Series in Synergetics book series (SSSYN, volume 1)


Basically, we may distinguish between two different kinds of chemical processes:
  1. 1)

    Several chemical reactants are put together at a certain instant, and we are then studying the processes going on. In customary thermodynamics, one usually compares only the reactants and the final products and observes in which direction a process goes. This is not the topic we want to treat in this book. We rather consider the following situation, which may serve as a model for biochemical reactants.

  2. 2)
    Several reactants are continuously fed into a reactor where new chemicals are continuously produced. The products are then removed in such a way that we have steady state conditions. These processes can be maintained only under conditions far from thermal equilibrium. A number of interesting questions arise which will have a bearing on theories of formation of structures in biological systems and on theories of evolution. The questions we want to focus our attention on are especially the following:
    1. 1)

      Under which conditions can we get certain products in large well-controlled concentrations?

    2. 2)

      Can chemical reactions produce spatial or temporal or spatio-temporal patterns?



Transition Rate Master Equation Malonic Acid Detailed Balance Soft Mode 
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  1. In this chapter we particularly consider the occurrence of spatial or temporal structures in chemical reactions. Concentration oscillation were reported as early as 1921 by C. H. Bray: J. Am. Chem. Soc. 43, 1262 (1921)CrossRefGoogle Scholar
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Deterministic Processes, Without Diffusion, One Variable 9.3 Reaction and Diffusion Equations

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Reaction-Diffusion Model with Two or Three Variables: the Brusselator and the Oregonator

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Stochastic Model for a Chemical Reaction Without Diffusion. Birth and Death Processes. One Variable

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Stochastic Model for a Chemical Reaction with Diffusion. One Variable

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Stochastic Treatment of the Brusselator Close to Its Soft Mode Instability

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Chemical Networks

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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