细胞新陈代谢的数学模型。自组织和 混沌

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摘要翻译：
利用非线性动力学的经典工具，借助球形节杆菌转化类固醇的数学模型，研究了细胞内代谢过程中的自组织过程和混沌现象。我们构造了在动膜电位耗散变化情况下得到的相参量图。所得振荡模分为正则吸引子和奇异吸引子。我们计算了系统发生自组织和混沌的分叉，以及“混沌-有序”、“有序-混沌”、“有序-有序”和“混沌-混沌”的跃迁。发现了Feigenbaum的情景和间歇性。对于一些选定的模，构造了吸引子的相图投影、Poincar截面和Poincar映射。计算了所研究模式的Lyapunov指数的总谱。证明了吸引子的结构稳定性。在给定的新陈代谢过程中，在细胞中形成规则的和奇怪的吸引子的一般情况被发现。研究了它们在代谢过程中出现的物理本质。
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英文标题：
《A mathematical model of the metabolism of a cell. Self-organization and
  chaos》
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作者：
V.I. Grytsay, I.V. Musatenko
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最新提交年份：
2018
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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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, Poincar\'e sections, and Poincar\'e 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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PDF链接：
https://arxiv.org/pdf/1802.02546

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关键词：新陈代谢 数学模型 自组织 Organization Quantitative obtained mathematical study 研究 计算