流网络中拓扑控制的涌现动力学
Topologically controlled emergent dynamics in flow networks
摘要：
流动网络对于生物体和工程系统都是必不可少的。这些网络通常呈现出复杂的动态，至少部分地由其拓扑结构控制。以前的工作表明，拓扑复杂的网络互连明确的振荡或兴奋的元素可以显示丰富的新兴动态。在这里，我们提出了一个复杂的流动网络的非线性电导，允许内部积累/消耗的体积，没有任何固有的振荡或兴奋的行为在节点上的模型。在没有任何时间依赖性的压力输入和输出，我们观察到新兴的动力学的形式，通过系统的自我维持波。这些波的频率在很大程度上取决于网络架构，并且可以用拓扑度量来解释。
英文摘要：
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks interconnecting explicitly oscillatory or excitable elements can display rich emerging dynamics. Here we present a model for complex flow networks with non-linear conductance that allows for internal accumulation/depletion of volume, without any inherent oscillatory or excitable behavior at the nodes. In the absence of any time dependence in the pressure input and output we observe emerging dynamics in the form of self-sustained waves, which travel through the system. The frequency of these waves depends strongly on the network architecture and it can be explained with a topological metric.
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