随机网络上物质流系统的稳定性和动力学性质
Stability and dynamical properties of material flow systems on random networks
摘要：
运用复杂网络和无序系统理论，研究了随机图上物质流网络的稳定性和动力学性质。特别是，我们解决的不稳定性，在经济，生态和生物系统的流动网络的特点。基于随机矩阵理论的结果，我们给出了定义在广连通随机图上的这类系统的相图，并详细研究了控制策略的选择和网络结构对稳定性的影响。我们还提出了基础图的更复杂的拓扑结构的结果，重点是连通的Erdös-Réyni图，小世界网络和Barabási-Albert无标度网络。结果表明，投入产出矩阵元素的可变性，以及基础图形的随机结构往往使系统不太稳定，而快速的价格动态或对股票积累的强烈反应促进稳定性。
英文摘要：
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.
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