论文标题
自催化网络：网络拓扑与动态之间的紧密关系
Autocatalytic Networks: An Intimate Relation between Network Topology and Dynamics
论文作者
论文摘要
我们研究一个自闭症反应网络家族，我们称之为高链，这是超囊的概括。超链和相关的动力系统称为复制器方程，是大分子进化的可能机制，并提议在益生元化学的生命起源中发挥作用。进化游戏动力学，遗传选择以及Lotka-volterra的生态学方程也发生了相同的动力系统。超链中的箭头封装了一种物种对另一种物种自催化复制的酶促影响。我们表明，捕获所有此类酶促影响的超链的网络拓扑与其生成的质量作用系统的动力学特性密切相关。诸如正平衡和永久性的存在，唯一性和稳定性之类的动力学特性取决于图理论特性，例如存在跨度线性子图的存在，无根，循环和汉密尔顿。
We study a family of networks of autocatalytic reactions, which we call hyperchains, that are a generalization of hypercycles. Hyperchains, and the associated dynamical system called replicator equations, are a possible mechanism for macromolecular evolution and proposed to play a role in abiogenesis, the origin of life from prebiotic chemistry. The same dynamical system also occurs in evolutionary game dynamics, genetic selection, and as Lotka-Volterra equations of ecology. An arrow in a hyperchain encapsulates the enzymatic influence of one species on the autocatalytic replication of another. We show that the network topology of a hyperchain, which captures all such enzymatic influences, is intimately related to the dynamical properties of the mass action system it generates. Dynamical properties such as existence, uniqueness and stability of a positive equilibrium as well as permanence, are determined by graph-theoretic properties such as existence of a spanning linear subgraph, being unrooted, being cyclic, and Hamiltonicity.
