复杂网络节点重要性与星型网控制研究

发布时间：2018-01-04 01:25

本文关键词：复杂网络节点重要性与星型网控制研究　出处：《闽南师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：本文基于复杂网络的同步性理论、严格可控性理论和控制能量理论,研究了网络同步中节点重要性分析、一类星型网的严格可控性和星型网的控制能量问题。首先,基于网络节点收缩方法,研究了网络同步中节点重要性问题。根据复杂网络的图谱理论,从理论的角度分析了三种规则无向网节点收缩前后的网络同步能力变化,最后发现节点收缩后网络的同步能力均是增强的。然而数值仿真却发现在BA无标度网和WS小世界网中同时存在使网络同步能力增强和减弱的节点。其次,基于复杂网络的严格可控性理论,研究了一类星型网的严格可控性问题。构造了一条链状的星型网络,基于一种特殊的标号技巧和递归方法,从理论上给出了该类网络的特征多项式的严格表达式。从该表达式中可以直接给出网络严格可控性相关结果:这类网络的严格可控性完全由它的零特征值决定。最后,基于复杂网络的控制能量理论,利用严格的控制输入矩阵,研究了星型无向网的控制能量问题。发现了一个共同的结论:控制系统需要不断消耗能量,但随着时间的推移,所需要消耗的能量逐渐减少,最终趋向于一个常数值。数值仿真结果证明了该理论的有效性。
[Abstract]:The synchronization of complex network theory based on strict controllability theory and energy theory, studies the importance of nodes in network synchronization analysis, strictly controlled and star network control problem of a star type energy network. Firstly, the network node contraction method based on the problem of node importance. According to the theory of network synchronization the complex network, from the perspective of the theory of three kinds of rules without changes to the network synchronization ability before and after the contraction of the network node, and finally found the synchronization network node contraction is enhanced. However, the numerical simulation was found in the BA scale-free network synchronization node to increase and decrease in the presence of small world network and WS in the net at the same time. Secondly, strictly controlled based on complex network theory, studies the problem of strict controllability for a star shaped network. To construct a chain star network, based on a special Labeling techniques and special recursive method, gives the strict expression of characteristic polynomial of this kind of networks theoretically. From the expression can directly give the network strictly related to controllability results: strict controllability of this type of network is completely determined by its zero eigenvalues. Finally, based on the theory of energy control of complex networks. The control input matrix strictly, on the star type to control energy network. Found a common conclusion: control system needs to consume energy, but with the passage of time, the amount of energy required to gradually reduce, finally tends to a constant value. Numerical simulation results prove the effectiveness of the the theory.

【学位授予单位】：闽南师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O157.5

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