# Dynamical properties of models for the Calvin cycle

Source: [Dynamical properties of models for the Calvin cycle](<https://www.sota2.com/research/paper/68fa51f71e209131ce977354>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:38:10.632Z

Authors: Alan D. Rendall, Juan J. L. Velazquez

Published: 2013-03-14T21:53:08.000Z

## Abstract

Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric coefficients and chemical kinetics and whether or not diffusion is taken into account. This paper studies the long-time behaviour of solutions of several of these systems, concentrating on the ODE case. In some examples it is shown that there exist two positive stationary solutions. In several cases it is shown that there exist solutions where the concentrations of all substrates tend to zero at late times and others (runaway solutions) where the concentrations of all substrates increase without limit. In another case, where the concentration of ATP is explicitly included, runaway solutions are ruled out.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1303.3621>)

[PDF](<https://arxiv.org/pdf/1303.3621.pdf>)