细胞新陈代谢的数学模型。自组织与混沌
A mathematical model of the metabolism of a cell. Self-organization and chaos
摘要：
本文利用非线性动力学的经典工具，借助球形节杆菌转化甾体的数学模型，研究了细胞代谢过程中的自组织过程和混沌现象。我们构建了在动力学膜电位耗散的变化下获得的相参数图。得到的振荡模式被分为规则和奇怪的吸引子。计算了系统发生自组织和混沌的分岔，以及混沌-有序、有序-混沌、有序-有序和混沌-混沌的转变。对于某些特定的模式，构造了吸引子的相图、Poincaré截面和Poincaré映射的投影。计算了所研究的模式的李雅普诺夫指数的总谱。证明了吸引子的结构稳定性。本文给出了细胞在特定代谢过程中形成规则吸引子和奇异吸引子的一般情形，并研究了它们在代谢过程中出现的物理性质。
英文摘要：
Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and strange attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-order", "order-chaos", "order-order", and "chaos-chaos" arise. Feigenbaum's scenarios and the intermittences are found. For some selected modes, the projections of the phase portraits of attractors, Poincaré sections, and Poincaré maps are constructed. The total spectra of Lyapunov indices for the modes under study are calculated. The structural stability of the attractors is demonstrated. A general scenario of the formation of regular and strange attractors in the given metabolic process in a cell is found. The physical nature of their appearance in the metabolic process is studied.
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