Study On The Structural Controllability Of Temporal And Complex Networks

The ultimate proof of our understanding and applications of natural or techno-logical systems is reflected in our ability to control them, and structural controllability is one of the approach to study and understand the topology properties from the per-spective of control theory. With the blossoming study of complex networks in last decade, structural controllability has attracted great and wide attentions of researchers from fields vary from biology and physics to sociology and economy because of its paramount importance in science and engineering applications, and past few years have witnessed plentiful fruits on it. The advancement of wireless communication technol-ogy and development of digital service provide us much easier methods to record and store huge amount of data, such as the information regarding human social activities and on-line interacting behaviors. Networks generated by these data are called tempo-ral networks, whose nodes and interactions may strengthen, weaken, appear and dis-appear at various time scales. Most networks in our economy, nature and society can be represented by temporal networks, and a large number of studies indicate that this kind of networks have great influence on our daily life and social behaviors. Although our knowledge and understandings of temporal networks have been strengthened and deepened, the study on structural controllability of temporal networks is still a blank. Therefore, in order to widen our understandings of temporal structures and improve our ability to control them, this thesis will focus on this untouched topic by theoretical analysis and numerical simulations.Based on the structural controllability and the temporal properties, we specifically study the structural controllability and controlling centrality of temporal networks. The main contents of this paper are organized as follows:· We study the structural controllability of temporal networks by improving the Maximum Matching method used in the static cases, which is called Priority Maximum Matching (PMM) method in this paper. This part of contents is pre-sented in chapter 3 in details. We first split a temporal network into a sequence of characteristic intervals under its characteristic time, and get a sequence of characteristic graph within each characteristic interval. Then we collect out the maximum characteristic graphs from the sequence of characteristic graph. Last we apply our improved Priority Maximum Matching method to these maximum characteristic graphs. With the analysis of numerical simulations on the temporal networks generated by two categories of empirical datasets, we find the control efficiency varies from different priority sequences, and moreover, this improved method retains as much temporal information as possible.· Similar to the description of a static network by the Linear Time-Invariant (LTI) system, we associate a temporal network with the Linear Time-Variant (LTV) system to study its structural controllability. The detailed content is presented in chapter 4. We first apply the non-periodic sampling process to the LTV system associated with a temporal network and on this basis we define the controlling centrality, i.e the maximum controllable subspace, of temporal network. Then we further transform a temporal network into a static, non-cyclic and directed one by Time-Ordered Graph (TOG) model, and find out the Breadth First Search (BFS) trees and its corresponding temporal trees in the original temporal network. This equivalent transformation allows us to understanding the complicated product of matrices by simple reachability vectors of temporal trees.· On the basis of TOG model and the reachability vectors of temporal trees given in chapter 4, we give the analytical bounds (both lower and upper) of controlling centrality in chapter 5. By classifying temporal trees into two categories and four different types, we study each type of temporal trees and give an analytical bounds of controlling centrality within a specified type. With these bounds we further give the controlling centrality of the node in a temporal network. Finally, we verify our results by both artificial temporal networks and realistic temporal networks generated by three categories of empirical datasets, and we find out some interesting relationship and phenomenon.