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Dynamics of small autocatalytic reaction networks—I. bifurcations, permanence and exclusion

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Abstract

Catalysis in replication networks has become an important issue in biophysics and other areas of biology. Examples are RNA catalysis, idiotype recognition in the immune response and dynamical models of Maynard-Smith games in sociobiology.

Chemical reaction networks describing catalysed, template-induced reproduction of three species are analysed in full generality. The nine-dimensional parameter space is reduced to three relevant angular coordinates which determine completely the phase portraits (PPs) and the bifurcation patterns. All cases are classified and all generic as well as most of the nongeneric transitions are listed and described.

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Authors and Affiliations

  1. Institut für theoretische Chemie der Universität Wien, Währingerstraße 17, A 1090, Wien, Austria

    Peter F. Stadler & Peter Schuster

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  1. Peter F. Stadler
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  2. Peter Schuster
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Stadler, P.F., Schuster, P. Dynamics of small autocatalytic reaction networks—I. bifurcations, permanence and exclusion. Bltn Mathcal Biology 52, 485–508 (1990). https://doi.org/10.1007/BF02462263

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  • DOI: https://doi.org/10.1007/BF02462263

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