论文标题
随机反应网络的分类和阈值动力学
Classification and threshold dynamics of stochastic reaction networks
论文作者
论文摘要
随机反应网络（SRN）提供了许多现实世界网络的模型。例子包括流行病学，药理学，遗传学，生态学，化学和社会科学网络。在这里，我们通过连续时间马尔可夫链（CTMC）对随机反应网络进行建模，并特别注意一维质量表演SRNS（1-D Stotoechiementric Subspace）。我们对1-D SRN的基础CTMC的所有状态进行了分类。在（多达四个参数）方面，我们为SRN的各种动力学特性（包括爆炸性，复发性，过时，千古性和准平台分布的尾巴渐近性）提供了尖锐的可检查标准。结果，我们证明了所有1-D内属性网络都是非爆炸性的，并且复发性具有呈层状的固定分布，并带有Conley-Maxwell-Poisson（CMP）类似的尾巴，前提是相关的CTMC的状态空间包括封闭式封闭类的相关CTMC的状态空间。特别是，我们在一个维度上证明了最近提出的正复发猜想：具有1-D化学计量学子空间的弱可逆的质量表演SRN是正复发。主要结果的证明取决于我们最近对具有多项式过渡速率函数的CTMC的工作。
Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by continuous time Markov chains (CTMCs) and pay special attention to one-dimensional mass-action SRNs (1-d stoichiometric subspace). We classify all states of the underlying CTMC of 1-d SRNs. In terms of (up to) four parameters, we provide sharp checkable criteria for various dynamical properties (including explosivity, recurrence, ergodicity, and the tail asymptotics of stationary or quasi-stationary distributions) of SRNs in the sense of their underlying CTMCs. As a result, we prove that all 1-d endotactic networks are non-explosive, and positive recurrent with an ergodic stationary distribution with Conley-Maxwell-Poisson (CMP)-like tail, provided the state space of the associated CTMCs consists of closed communicating classes. In particular, we prove the recently proposed positive recurrence conjecture in one dimension: Weakly reversible mass-action SRNs with 1-d stoichiometric subspaces are positive recurrent. The proofs of the main results rely on our recent work on CTMCs with polynomial transition rate functions.
