Stability of stationary solutions in models of the Calvin cycle

TL;DR

This paper investigates the number and stability of positive stationary solutions in simplified models of the Calvin cycle, revealing conditions for multiple solutions and their stability properties.

Contribution

It provides new results on the existence and stability of stationary solutions in Calvin cycle models, including bifurcation analysis and parameter conditions.

Findings

Existence of two positive stationary solutions in certain parameter regions.

One solution can be asymptotically stable while the other is unstable.

Under specific conditions, a continuum of solutions exists.

Abstract

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.