半格网络的动力学
The Dynamics of Semilattice Networks
摘要：
有限状态空间上的时间离散动力系统已被成功地用于模拟自然和工程系统，如生物网络，社交网络和工程控制系统。它们具有直观的优势，在大多数情况下，模型可以很容易地在计算机上模拟;然而，除了模拟之外，很少有分析工具可用。本文的动机是开发这样的工具，在生物学模型的分析。在本文中，我们已经确定了广泛的一类离散动力系统与有限的相空间，其中一个可以得出强有力的结果，他们的长期动态的性质，他们的依赖图。对具有强连通依赖图的半格网络的极限环进行了完全分类，并给出了一般情况下的多项式上界和下界。
英文摘要：
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being intuitive and models can be easily simulated on a computer in most cases; however, few analytical tools beyond simulation are available. The motivation for this paper is to develop such tools for the analysis of models in biology. In this paper we have identified a broad class of discrete dynamical systems with a finite phase space for which one can derive strong results about their long-term dynamics in terms of properties of their dependency graphs. We classify completely the limit cycles of semilattice networks with strongly connected dependency graph and provide polynomial upper and lower bounds in the general case.
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