糖酵解模型的动力学分析

Dynamical Analysis of the Glucose Zymolysis Model

主要研究了糖酵解模型由产物ADP流出速率常数2σ引起的Hopf分岔,探讨了糖酵解过程中广泛存在的振荡现象产生的原因.首先研究了平衡点的个数,然后利用Lyapunov稳定性定理研究了平衡点的稳定性,最后利用Hopf分岔理论研究了其Hopf分岔.证明了该Hopf分岔是已发现的糖酵解过程中广泛存在的振荡现象(即周期解)产生的原因,即参数2σ在其临界值2σc处模型会发生超临界Hopf分岔,分岔出稳定的周期解.并利用软件WinPP进行了数值模拟,结果与理论分析相吻合.

The Hopf bifurcation is mainly studied,which is induced by the leaving rate,σ2,of the ADP in the glucose zymolysis model.And the cause of the extensively existing oscillation phenomena in the process of the glucose zymolysis is also discussed.At first,the number of the equilibria is considered.Then,their stability is established by the Lyapunov stability theory.At last,the Hopf bifurcation of the equilibrium induced by the parameter σ2 is obtained by the Hopf bifurcation theory.The result proves that this Hopf bifurcation is the cause of the extensively existing oscillation phenomena （i. e. , periodic solution） in the process of the glucose zymolysis, i. e. , the glucose zymolysis model undergoes the supercritical Hopf bifurcation at the critical value σ2c of the parameter σ2 and a stable periodic executed by employing the software WinPP alytical ones. solution bifurcates. And the numerical and the numerical results agree very well simulation is with the analytical ones.