基于复杂网络知识的分数阶信息传播动力学行为分析

信息技术的高速发展促进了以互联网为典型代表的网络技术的蓬勃发展，这些有形或无形的复杂网络种类繁多，以不同的形式存在于现实世界中，并影响着人类生活的方方面面。分数阶导数具有全局相关性，且能体现系统函数发展的历史依赖过程，分数阶导数模型弥补了整数阶模型理论与实验结果吻合欠佳的缺点。因此利用分数阶微积分理论来研究复杂网络的信息传播动力学行为具有重要的理论意义和应用价值。本项目综合多学科知识，引入基于系统建模—动力学行为分析—系统行为控制的一体化研究思路.首先利用分数阶微积分理论针对不同拓扑结构的复杂网络系统进行建模并进行相应的动力学行为分析，诸如信息传播阈值、范围和同步等；然后进而考虑网络拓扑结构对相应系统的动力学行为的影响；最后结合现代控制理论探讨相应复杂网络系统的可控性，以及如何实现对系统的某些品质和特征进行增强和削弱控制，为进一步研究分数阶微积分理论在实际复杂网络中应用提供理论基础和支持。

With the rapid development of modern information technology, the network technology, the Internet as a typical representative, has also been booming. various types of complex networks in various forms exist in the real world, and affect every aspect of human life..Fractional order derivative is global correlation, and can reflect the history of the development of system function depend on the process. The fractional-order derivative model can overcome the disadvantages that the experimental findings is not consistent with the result of integer derivative one. The resarch of fractional calculus has been attracted great attention of many researchers. And the results can be widely applied into many areas. So it has important theoretical significance and practical application value to study the dynamical behaviors of complex ntework using fractional calculus theory. .The project integrated multidisciplinary knowledge, introduced the integration of research ideas which based on the system modeling, dynamic behavior analysis and system behaviors control. Firstly, using the theory of fractional order calculus, we will give the system models for different topology structure of the complex network, and discuss the corresponding dynamic behaviors and characters, such as the information transportation, synchronization and so on. Then consider the network topology structure on the influence of the dynamic behaviors of the corresponding system. Finally, combined the modern control theory, we will explore corresponding complex network system controllability and inquiry some suitable control method or rule which can realize some requirement in reality. The expected results of this project will provide a theory which can guarantee that the fractional order model can be widely applied in some real networks and other fields.