时空混杂社团网络的同步研究

项目名称： 时空混杂社团网络的同步研究

项目编号： No.11502139

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 柴元

作者单位： 上海电力大学

项目金额： 20万元

中文摘要： 社团结构作为理解复杂网络细观特征的一个关键因素，已经成为了复杂网络研究领域的关键科学问题。对社团网络的时空和混杂特征的研究，有助于揭示非线性动力学等诸多学科中普遍存在的一般规律。为建立时空混杂社团网络，需要深入认识时空耦合网络的动力学特性，相关科学问题是时空混杂社团网络的建模、控制和识别，是非线性动力学领域的重要前沿课题。本项目运用主稳定函数判据、主动滑模和Lasalle不变原理等方法，通过动力学建模、理论分析和数值仿真，研究时空混杂社团网络的非线性动力学行为。同时计入时间延迟、未知参数等影响因子，研究由不同时滞且参数未知节点构成的社团网络的辨识和同步问题。本项目的研究还将通过应用经典的控制理论，设计有效的控制识别方案和时空耦合强度的自适应率，并对时空混杂社团网络加以控制。研究成果将丰富非线动力学的研究对象，扩展非线性动力学的研究领域，为工程系统的优化控制策略、提高同步效率奠定理论基础。

中文关键词： 混沌控制；时空混杂社团网络；时滞；同步控制；参数识别

英文摘要： Community structure is a key in mesoscopic structural properties of complex networks, has become key scientific issues in the research area of complex work. In fact, researches on the spatiotemporal and mixed characteristics of community networks will help to unveil the general laws in nonlinear dynamics, etc. To establish spatiotemporal mixed community networks, the dynamical characteristics of the spatiotemporal coupled networks should be fully understood. The corresponding scientific issue is the modeling, control and identification of spatiotemporal mixed community networks, which is a significant topic at the forefront of the field of nonlinear dynamics. Based on the master stability function criterion, active sliding mode control strategy, Lasalle invariance principle, nonlinear dynamical behaviours of spatiotemporal mixed community networks will be investigated via dynamic modelling, theoretical analysis and numerical simulations. A novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed mixed community networks with non-identical nodes is initiated by adding time delay and unknown parameters. Based on the classical control theory, a criterion is established for synchronization of spatiotemporal mixed community networks by constructing an effective control identification scheme and adjusting the adaptive coupling strength automatically. The research results of this project will develop the research subjects of nonlinear dynamics, expand research fields of nonlinear dynamics, lay the theoretical foundation of optimizing control strategies of engineering systems, and improve the efficiency of the synchronization.

英文关键词： Chaos Control;Spatiotemporal Mixed Community Networks;Time Delay;Synchronization Control;Parameter Identification