Abstract

We analyze the nonlinear dynamics of an isothermal system involving complex enzymatic reactions for L-DOPA (L-3,4-dihydroxyphenylalanine) production by numerical simulation. The mass action kinetics of the system forms a family of 9ordinary differential equations with 22 parameters. The multiple steady states are calculated by the chemical reaction network toolbox. Starting from one of the steady states, a limit point is guaranteed to be detected due to a change in the system parameters using the numerical continuation software MatCont. Other bifurcations are also obtained via the bifurcation continuations of the limit point, such as cusp bifurcations, Hopf bifurcations, limit cycles, zero Hopf bifurcations, generalized Hopf bifurcations, period-doubling, and so on. A transition of a period-doubling bifurcation to chaos occurs by numerical simulations. Positive values, 0.25~0.71, of Lyapunov exponents are obtained for the chaotic dynamics. Poincare maps and power spectrum densities are also plot. The Feigenbaum constant is computed to be 4.681~4.705.

中文翻译：

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涉及L-酪氨酸氧化生成L-DOPA的酶反应中多个稳态，极限环，加倍和混沌的数值分析

摘要

我们通过数值模拟分析了涉及L-DOPA（L-3,4-dihydroxyphenylalanine）生产的复杂酶反应的等温系统的非线性动力学。该系统的质量作用动力学形成具有22个参数的9个常微分方程族。多个稳态由化学反应网络工具箱计算。从一个稳态开始，由于使用数字连续软件MatCont改变了系统参数，可以确保检测到一个极限点。还可以通过极限点的分叉连续性来获得其他分叉，例如尖点分叉，Hopf分叉，极限环，零Hopf分叉，广义Hopf分叉，周期倍增等。通过数值模拟，发生了倍频分叉到混沌的过渡。Lyapunov指数为0.25〜0.71，为混沌动力学的正值。还绘制了Poincare图和功率谱密度。Feigenbaum常数经计算为4.681〜4.705。