在网络间相互依存关系日益增强的今天，单个网络上的动力学研究存在一定局 限性，为了更好地反映实际网络的演化机制，将这些动力学行为放在相互依存网络中研究就显得尤为重要。本项目将深入、系统地研究相互依存动态网络的动力学同步控制和骨干结构识别问题。具体内容包括：(1) 建立相互依存动态网络模型，基于Laplacian 矩阵特征值的性质，研究这些网络的分层同步问题；(2) 在中尺度框架下，探索网络的同步过程，揭示网络的同步演化规律和时空复杂性；(3)分析网络在时滞或噪声作用下的动力学行为，研究设计合适的控制器确保网络的响应具有理想的性能，给出相应的分层同步的理论框架和刻画指标；(4) 探讨在骨干结构未知或部分未知的情况下，设置控制器，利用外同步的方法反演网络的骨干结构。这些问题的研究是目前复杂网络研究新的探索和深入发展，对于了解真实复杂网络信息过程，最终实现对网络行为的预测和控制提供坚实的理论基础。

Today, the interdependent relations is growing between the networks. It has certain limitations for the dynamical research on the single network. In order to show the evolution behavior and the mechanisms of the actual networks much better, the research of dynamical behavior in the interdependent networks is particularly important. This project will make a thorough systematic study on the dynamic synchronization,control and main structure identification of the interdependent networks. Concrete contents include: (1) Interdependence dynamic network model is established. And the hierarchical synchronization problems are investigated according to the eigenvalues of the Laplacian matrix. (2) According to the meso scale, the synchronization process of networks is explored, and they illustrate the evolvement of synchronization and the complexity of time and space of networks; (3) When the time delay or the noise is introduced in the networks, we will analyze and explore the dynamic behavior of this kind of network. We will design appropriate controllers to ensure that the response of the networks has the ideal performance, and gives the corresponding theoretical framework of the synchronization. (4) When the main structure of the networks is unknown or partially unknown, with the controllers, the main structure is identified. And at the same time,the external synchronizaiton is obtained between two interdependent networks. It is a new exploration and development in depth for the investigation of these problems. Furthermore, they will be solid theoretical basis for understanding the complicated information process of the real networks and predicting and controlling the network behavior ultimately.