Accuracy of a one-dimensional reduction of dynamical systems on networks
Accuracy of a one-dimensional reduction of dynamical systems on networks
复制标题
DOI：
10.1103/physreve.105.024305
复制
发表时间：
2022-02-11
影响因子：
2.4
通讯作者：
Masuda, Naoki
中科院分区：
文献类型：
--
作者：
Kundu, Prosenjit;Kori, Hiroshi;Masuda, Naoki
弹性是系统的一种能力，当系统受到干扰时，系统可以调整其活动以保持其功能。为了研究网络上的动态弹性，Gao等人[Nature (London) 530, 307(2016)]提出了一个理论框架，将网络上通常是高维的动态系统简化为一维动态系统。除了假设网络具有可忽略的程度相关性之外，这种一维还原的准确性依赖于三种近似。在本研究中，我们分析了假设没有度相关的网络的一维约简的准确性。我们这样做主要是通过检查作为方法基础的个别假设的有效性。在五个动力系统模型中，我们发现在大多数情况下，一维约简的准确性取决于状态变量的平衡值在节点上的扩散。具体来说，当节点状态的色散较小时，一维约简往往是准确的。我们还发现，节点状态与节点度之间的相关性与一维约简的准确性无关，这种相关性在网络上的各种动态系统中都很常见。
Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.