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A Calvin Bestiary

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Patterns of Dynamics (PaDy 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 205))

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Abstract

This paper compares a number of mathematical models for the Calvin cycle of photosynthesis and presents theorems on the existence and stability of steady states of these models. Results on five-variable models in the literature are surveyed. Next a number of larger models related to one introduced by Pettersson and Ryde-Pettersson are discussed. The mathematical nature of this model is clarified, showing that it is naturally defined as a system of differential-algebraic equations. It is proved that there are choices of parameters for which this model admits more than one positive steady state. This is done by analysing the limit where the storage of sugars from the cycle as starch is shut down. There is also a discussion of the minimal models for the cycle due to Hahn.

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Authors and Affiliations

  1. Institut für Mathematik, Johannes Gutenberg-Universität, Staudingerweg 9, D-55099, Mainz, Germany

    Alan D. Rendall

Authors
  1. Alan D. Rendall
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Correspondence to Alan D. Rendall .

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Editors and Affiliations

  1. Mathematical Institute, Free University of Berlin, Berlin, Germany

    Pavel Gurevich

  2. Mathematical Institute, Free University of Berlin, Berlin, Germany

    Juliette Hell

  3. Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA

    Björn Sandstede

  4. School of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA

    Arnd Scheel

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Rendall, A.D. (2017). A Calvin Bestiary. In: Gurevich, P., Hell, J., Sandstede, B., Scheel, A. (eds) Patterns of Dynamics. PaDy 2016. Springer Proceedings in Mathematics & Statistics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-64173-7_18

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