随机时滞动态网络的分岔控制与优化

Most of modern systems should be modeled as complex dynamic networks. The study towards dynamical control and optimization of complex dynamic networks becomes interesting and significant. In this project, we focus on the following two scientific problems of networks: 1.Improve the dynamical behavior, especially the bifurcate behavior of complex dynamic networks. 2. Optimize the topological structure of complex dynamic networks. Based on the two scientific problems above, the following subjects will be studied: Firstly, the topological models and dynamical models of dynamic networks will be built based on random factors and time delays, and some new quantities used to describe the topology of the given networks will be provided; Secondly, we will analyze the bifurcate behavior of dynamic networks by using the bifurcation theory of nonlinear systems, find out the key parameters of random factors and time delays which influence and further determine the occurrence of the bifurcation, and bring out the critical values of certain key parameters for the bifurcation; Thirdly, we will study how to control the bifurcate behavior of dynamic networks by using the chaotic control theory, find out the method to improve the bifurcate behavior of dynamic network, and bring out the corresponding control strategies; Finally, we will analyze the relationship between topological structures and bifurcation phenomena of the given networks. We will optimize the network structure based on the characteristics of bifurcation, and then improve the topological structure of dynamic networks. We have done part work about this project. So far some interesting results have been obtained. We believe that this project will be very useful in understanding the topological structures and bifurcating behaviors of dynamic networks.

现实生活中很多模型都可以用复杂动态网络来描述，对其动力学控制和优化问题的研究具有重要意义。本项目围绕如何改进动态网络的分岔行为、优化网络结构两个科学问题，首先结合实际建立基于随机和时滞耦合的动态网络模型，提出反映特定网络特性的新特征量；其次借助非线性系统的分岔理论研究动态网络的分岔问题，阐明随机和时滞对动态网络分岔行为的影响，确定发生分岔的参数临界值；然后将混沌控制的思想应用到动态网络模型中，控制网络的分岔行为，给出有效地改进网络动力学分岔的方法，并提出相应的控制策略；最后探讨动态网络的分岔行为和网络拓扑结构的内在关系，优化网络的拓扑结构和动力学分岔。本项目前期研究已取得重要进展，其最终研究成果有望提高对动态网络结构特性和动力学行为的认知水平。

本项目主要从复杂网络的动力学行为和网络结构两个方面开展研究。重点研究了复杂网络中的分岔、分岔控制和一致性问题，并就与之密切相关的网络级联动力学、节点牵制控制等问题进行探索。关于网络动力学：建立了具有分布时滞和强核的神经网络模型、具有隐含层的时滞网络模型、网络拥塞模型、变时滞切换忆阻神经网络模型，并针对具体模型选取特征参数，讨论了稳定性、分岔或分岔控制问题，并研究了与网络化多智能体系统的一致性问题；关于网络结构：讨论了相互依存网络的演化规律与级联行为，发现对不同结构的网络耦合而成的相互依存网络模型，仅攻击度数低的节点，也可以使网络迅速崩溃。为了优化控制不同结构的网络，讨论了网络的牵制控制（pinning control）问题，利用矩阵论中的Perron特征值与Perron特征向量，解决了现有牵制控制方法中很多节点出度入度相等时，控制节点的选取问题。 . 将复杂网络的结构和动力学行为相结合，进一步深入研究，无疑具有重要的理论意义和实际意义。本项目相关论文发表在IEEE Transactions on Cybernetics, Nonlinear Dynamics, Neurocomputing, Neural Networks, Physica A等期刊和重要国际会议上。