"An analysis of a mathematical model of a reaction-diffusion system"Gürbüz, BurcuIn this study, we consider an analysis of a mathematical model of a reaction-diffusion system which is representing the Calvin cycle, a crucial part of photosynthesis. By incorporating ATP diffusion into the model, a system of reaction-diffusion equations is derived. It is proved that, with appropriate parameter choices, there are numerous spatially inhomogeneous positive steady states. Furthermore, it is shown that all positive steady states, whether homogeneous or inhomogeneous, are shown to be nonlinearly unstable, except for a trivial steady state where all concentrations except ATP are zero. In the spatially homogeneous case, certain steady states exhibit non-real eigenvalues upon linearization, indicating the potential for oscillatory behavior. Numerical simulations further illustrate the solutions where the concentrations vary as non-monotonic functions of time. |
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