论文标题
糖酵解模型的无限解决方案
Unbounded solutions of models for glycolysis
论文作者
论文摘要
Selkov振荡器是对糖酵解的简单描述，是一个具有质量动力动力学的两个普通微分方程的系统。在先前的工作中，作者建立了该系统解决方案的几个属性。在本文中，我们将其扩展为证明该系统的解决方案在后期以振荡方式与无穷大。该系统最初来自Michaelis-Menten动力学的另一个系统。结果表明，像大规模动作一样，迈克尔尼斯 - 市政系统的解决方案以单调的方式与无穷大。还显示它可以接受亚临界型霍夫夫分叉，从而接受不稳定的周期性解决方案。我们讨论了无限的解决方案对Selkov振荡器的生物学相关性的怀疑，并将其与文献中的其他模型进行了比较。
The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This system was originally derived from another system with Michaelis-Menten kinetics. It is shown that the Michaelis-Menten system, like that with mass action, has solutions which diverge to infinity in a monotone manner. It is also shown to admit subcritical Hopf bifurcations and thus unstable periodic solutions. We discuss to what extent the unbounded solutions cast doubt on the biological relevance of the Selkov oscillator and compare it with other models in the literature.
