具有ATP扩散的Calvin循环模型分析
Analysis of a model of the Calvin cycle with diffusion of ATP
摘要：
分析了作为光合作用一部分的卡尔文循环的数学模型的动力学。由于模型中包含了ATP的扩散，得到了反应扩散方程组。证明了对于适当的参数选择，存在空间非齐次正定态，实际上是无穷多个。它还表明，所有的正平衡态，齐次和非齐次，是非线性不稳定的。唯一稳定的光滑稳态是一个平凡的稳态，除了ATP的浓度外，所有的浓度都是零。它被发现，在空间均匀的情况下，有稳定的状态的属性，该状态的线性化的特征值是不真实的，表明存在振荡。数值模拟显示的解决方案的浓度不是时间的单调函数。
英文摘要：
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.
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