Mathematical Research on Dynamical Robustness of Complex Networks

电力网络、互联网、生物网络、人类接触网络等都被认为是复杂网络。为了考虑网络功能故障的预防措施，重要的是要了解复杂网络如何抵御网络元件的故障。在这项研究中，我们集中在网络上的动力学行为所维持的网络功能。我们已经开发了网络鲁棒性分析的理论框架，并进行了应用。特别是，我们已经表明，具有少量的相互作用的元素可以是重要的，而不是枢纽元素在异质耦合振荡器网络。此外，我们应用我们的方法来分析具有复杂结构的生物网络和流行病传播的异质连接的补丁。

Power networks, the Internet, biological networks, human contact networks are regarded as complex networks. In order to consider preventive measures for a breakdown of network functions, it is important to understand how the complex networks are robust against the failure of network elements. In this research, we have focused on the network function maintained by dynamical behavior on the network. We have developed the theoretical framework for network robustness analysis and performed applications. In particular, we have shown that the elements which have a small number of interactions can be important rather than hub elements in heterogeneously coupled oscillator networks. Further, we applied our method to the analysis of biological networks with complex structure and epidemic spreading in heterogeneously connected patches.