Mathematical Research on Dynamical Robustness of Complex Networks

电力网络、互联网、生物网络、人际交往网络都被视为复杂网络。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对网元故障具有健壮性。在本研究中，我们主要关注网络上的动态行为所维持的网络功能。我们建立了网络健壮性分析的理论框架，并进行了应用。特别是，我们已经证明，在异质耦合振子网络中，具有少量相互作用的元件可能比中心元件更重要。进一步，我们将我们的方法应用于具有复杂结构和异质连通斑块中的传染病传播的生物网络的分析。

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.