  In this paper results are obtained concerning the number of positive
stationary solutions in simple models of the Calvin cycle of photosynthesis and
the stability of these solutions. It is proved that there are open sets of
parameters in a model of Zhu et. al. for which there exist two positive
stationary solutions. There are never more than two isolated positive
stationary solutions but under certain explicit special conditions on the
parameters there is a whole continuum of positive stationary solutions. It is
also shown that in the set of parameter values for which two isolated positive
stationary solutions exist there is an open subset where one of the solutions
is asymptotically stable and the other is unstable. In related models , for
which it was known that more that one positive stationary solution exists, it
is proved that there are parameter values for which one of these solutions is
asymptotically stable and the other unstable. A key technical aspect of the
proofs is to exploit the fact that there is a bifurcation where the centre
manifold is one-dimensional.
