American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021268
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Analysis of a model of the Calvin cycle with diffusion of ATP

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

* Corresponding author: Alan D. Rendall

Received  July 2021 Revised  September 2021 Early access November 2021

The dynamics of a mathematical model of the Calvin cycle, which is part of photosynthesis, is analysed. Since diffusion of ATP is included in the model a system of reaction-diffusion equations is obtained. It is proved that for a suitable choice of parameters there exist spatially inhomogeneous positive steady states, in fact infinitely many of them. It is also shown that all positive steady states, homogeneous and inhomogeneous, are nonlinearly unstable. The only smooth steady state which could be stable is a trivial one, where all concentrations except that of ATP are zero. It is found that in the spatially homogeneous case there are steady states with the property that the linearization about that state has eigenvalues which are not real, indicating the presence of oscillations. Numerical simulations exhibit solutions for which the concentrations are not monotone functions of time.

Citation: Burcu Gürbüz, Alan D. Rendall. Analysis of a model of the Calvin cycle with diffusion of ATP. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021268
References:

show all references

References:
Non-monotone behaviour near $P_1$
">Figure 2.  Long-time behaviour of the solution in Fig. 1
Long-time behaviour of a solution approaching the point $P_2$
Plot in the $x_{\rm GAP}$-$x_{\rm Ru5P}$ plane of a solution starting near $P_2$

2020 Impact Factor: 1.327