复杂网络的分岔、混沌及其控制

Some basic tools, such as the bifurcation theory, the normal form theorem and center manifold theory of functional differential equations and control theory in engineering technique, etc., will be applied to investigate the stability, the existence of bifurcation, the properties of bifurcation of complex networks. First, we investigate the stability and the properties of bifurcation of complex networks with leakage delays. Secondly, we study the time-feedback control problem of delayed complex networks with delays (including leakage delay). Finally, we consider the controls of chaos in complex networks. By means of Matlab software, computer simulations for justifying the rationality of theoretical results are carried out. Meanwhile, we will foucs on what effect the delays of complex network models have on the dynamics of networks. The investigation of the project will provide some effective thinking of analysis and simulation technique to deal with what the delays of complex network models have effect on the dynamical behaviors of systems and further enrich the bifurcation theory of functional differential equations and control theory in engineering technique, meanwhile, it also promote the development of the related subjects. The theoretical findings will helpful in governing the laws of the change and development of complex networks, controlling and optimizing networks. It can also provide us the theoretical guide and decision-making basis. Thus the investigation on bifurcation, chaos of complex networks and their controls has important theoretical value and considerable significance of application.

本项目拟运用泛函微分方程的分岔理论、中心流形和规范型理论和工程技术中的控制理论等工具来研究复杂网络的稳定性、分岔存在性及分岔特性、分岔控制、混沌控制等问题。首先研究具有漏泄时滞的复杂网络模型的稳定性和分岔特性, 其次研究具有时滞(包括漏泄时滞)的复杂网络模型的分岔的反馈控制问题, 最后研究复杂网络模型的混沌控制问题。利用Matlab 软件进行计算机仿真验证理论结果的合理性, 同时关注复杂网络模型的时滞对所研究的复杂网络模型的动力学行为的影响。本项目的研究将为处理复杂网络模型的时滞(或其他参数)对系统的动力学行为的影响提供一些有效的分析思路和仿真技术, 进一步丰富泛函微分方程的分岔理论和工程技术的控制理论并促进相关学科的发展。理论分析所得结果将为我们掌握复杂网络的变化发展规律、控制和优化网络提供理论指导和决策依据。因此,复杂网络的分岔、混沌及其控制的研究具有重要的理论意义和现实的应用价值。