  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.
