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The Kerner linearization method

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Abstract

We examine in detail Edward Kerner’s method for linearizing the equations of enzyme kinetics. Our main result is the determination of canonical forms for systems which can be linearized by the method. This is done both in general and in the special cases of two and three dimensions where complete results are obtained.

The practical problem of identifying linearizable systems is also considered and computable necessary criteria are presented.

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Literature

  • Kerner, E. 1972. “A Dynamical Approach to Chemical Kinetics: Mass-Action Laws as Generalized Riccati Equations.”Bull. Math. Biophysics,34, 243–275.

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  • Pontriagin, L. 1946.Topological Groups. Princeton: Princeton Univ. Press.

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Authors and Affiliations

  1. School of Mathematics, Trinity College Dublin, Dublin 2

    Hedley C. Morris

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  1. Hedley C. Morris
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Morris, H.C. The Kerner linearization method. Bltn Mathcal Biology 36, 67–76 (1974). https://doi.org/10.1007/BF02461192

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  • DOI: https://doi.org/10.1007/BF02461192

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