论文标题
Selkov糖酵解模型中稳定极限周期的瞬态行为：生理障碍
Transient behaviour towards the stable limit cycle in the Selkov model of Glycolysis: A physiological disorder
论文作者
论文摘要
塞尔科夫（Selkov）在历史上提出了一种复杂糖酵解过程的简化模型。它显示了稳定的极限周期的存在，作为庞贝里 - 弯曲定理的一个例子。这种极限周期不过是消除正常/健康人的腺苷 - 磷酸腺苷（ADP）和果糖-6-磷酸（F6P）的时间的时间。与此极限周期的偏差相当于正常生理行为的偏差。如果偏离糖酵解稳定的极限周期，知道人体将需要多长时间才非常重要。但是，到目前为止，尚未详细研究收敛时间，具体取决于不同的初始参数值。这对于了解偏离正常周期的患病患者的恢复时间可能非常重要。这里已经在原始Selkov模型中计算了不同初始条件的收敛时间。据观察，收敛时间是距极限循环距离的函数，从循环中饱和。这个结果似乎是一种生理障碍。已经提出了一种将其纳入Selkov模型的可能的数学方法。
A simplified model for the complex glycolytic process was historically proposed by Selkov. It showed the existence of stable limit cycle as an example of Poincare-Bendixson theorem. This limit cycle is nothing but the time eliminated Lissajous plot of the concentrations of Adenosine-diphosphate (ADP) and Fructose-6-phosphate (F6P) of a normal/healthy human. Deviation from this limit cycle is equivalent to the deviation of normal physiological behaviour. It is very important to know how long a human body will take to reach the glycolytic stable limit cycle, if deviated from it. However, till now the convergence time, depending upon different initial parameter values, was not studied in detail. This may have great importance in understanding the recovery time for a diseased individual deviated from normal cycle. Here the convergence time for different initial conditions has been calculated in original Selkov model. It is observed that convergence time, as a function of the distance from the limit cycle, gets saturated away from the cycle. This result seems to be a physiological disorder. A possible mathematical way to incorporate this in the Selkov model, has been proposed.
