自催化网络：网络拓扑与动力学的紧密联系
Autocatalytic Networks: An Intimate Relation between Network Topology and Dynamics
摘要：
我们研究一族自催化反应网络，我们称之为超链，它是超循环的推广。超链和相关的动力系统称为复制子方程，是大分子进化的一种可能机制，并被认为在生命起源中发挥作用。同样的动力系统也出现在进化博弈动力学、遗传选择和生态学的洛特卡-沃尔泰拉方程中。超链中的箭头封装了一个物种对另一个物种的自催化复制的酶促影响。我们发现，网络拓扑结构的超链，它捕获所有这样的酶的影响，是密切相关的动力学性质的质量作用系统，它产生。正平衡点的存在性、唯一性、稳定性和持久性等动力学性质由生成线性子图的存在性、无根性、循环性和Hamilton性等图论性质决定。
英文摘要：
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.
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