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| 摘要: |
| 在网络间相互依存关系日益增强的今天，如何挖掘网络间的相互依存关系（骨干结构）是相互依存网络研究中的重中之重。本文探讨了由两个子网构成的有向相互依存网络的骨干结构识别问题。在该网络中，本文只考虑子网间的耦合连接，不涉及子网的内部结构，同时，网络的耦合函数为非线性有界函数。基于李雅普诺夫稳定性理论、自适应同步控制技术和线性矩阵不等式（LMI）方法，本文提出了使得驱动网络和响应网络达到自适应同步的充分条件。这些条件使得在网络达到同步的同时，获得驱动网络的骨干结构的识别。最后的数值模拟验证了本文所提出的理论的正确性和有效性。 |
| 关键词: 有向相互依存网络 骨干结构识别 自适应同步 LMI 李雅普诺夫稳定性理论 |
| DOI： |
| 分类号:O231.9 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| Synchronization-based backbone structure identification for directed interdependent networks |
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CHEN Jieyi,TU Lilan
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| Abstract: |
| Today, with the increasing interdependent relationship emerged between networks, how to explore this kind of interdependence (i.e. backbone structure) become the most important research for interdependent networks. In this paper, the problem of backbone structure identification for directed interdependent networks is investigated, which is composed of two subnets. In this network, we only consider the backbone structure between subnets, but not involve the internal structure of the subnet. At the same time, the coupling function of the network considered is a nonlinear bounded. Based on Lyapunov stability theory, adaptive synchronization and control technology and linear matrix inequality method, some sufficient conditions for the adaptive synchronization of drive network and response network are proposed in this paper. These conditions enable us to identify the backbone structure of the drive network while the networks obtain their synchronization. Finally, some numerical simulations verify the correctness and effectiveness of the theory presented in this paper. |
| Key words: Directed interdependent networks Backbone structure identification Adaptive synchronization LMI Lyapunov stability theory |
