Krebs圈稳定性研究中的Lyapunov指数和Poincaré映射
Lyapunov Indices and the Poincaré Mapping in a Study of the Stability of the Krebs Cycle
摘要：
在建立数学模型的基础上，我们继续研究了代谢三羧酸循环。第一次，我们认为它的一致性和稳定性，这取决于耗散的跨膜电位形成的呼吸链在细胞质膜。根据给定的参数的ATP水平的动态的相位参数特性的构造。提出了多个自周期模和混沌模的形成方案。构造了Poincaré截面和映射。研究了模式的稳定性和分岔的分形性。计算了奇异吸引子的李雅普诺夫指数、发散度、KS熵、可预测性视界和李雅普诺夫维数的全谱。一些结论的结构-功能的连接确定依赖的细胞呼吸周期的三羧酸循环和电子传递链的功能的同步。
英文摘要：
On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxilic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane potential formed by the respiratory chain in the plasmatic membrane of a cell. The phase-parametric characteristic of the dynamics of the ATP level depending on a given parameter is constructed. The scenario of formation of multiple autoperiodic and chaotic modes is presented. Poincaré sections and mappings are constructed. The stability of modes and the fractality of the obtained bifurcations are studied. The full spectra of Lyapunov indices, divergences, KS-entropies, horizons of predictability, and Lyapunov dimensionalities of strange attractors are calculated. Some conclusions about the structural-functional connections determining the dependence of the cell respiration cyclicity on the synchronization of the functioning of the tricarboxilic acid cycle and the electron transport chain are presented.
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