Study On The Propagation Immunization In Target Control Of Complex Network

Control of complex network reflects human’s comprehension of complex system and the ability to reform it. The author explores the evolution model of complex network is very helpful, we can explain many different phenomenon which is belong to various fields of complex network conditions. To a great degree, the purpose of explaining phenomenon is to predict, and hope to be able to control.Putting forward along with the problem of the controllability in network, the complicated network and complex system about the control method research has become a hot issue.Whether complex networks and a variety of complex systems is controlled, or the feedback control, can realize the feedback control,, how to become fuzzy control and precisely control, such problems as how to achieve the minimum cost control and spontaneous controllability, which has a broad scientific significance. The research is of great value.Up-to-date research establishes the theory of target control of complex network becomes a hot issue in complex network field. The theory could find that one node can control a set of target nodes if the path length to each target node is unique.However, we find that this theory does not include the immune node or failure node which blocks the control signal. Following the advantages of the theory, we use method to immune those nodes of the set for target nodes, which called isolation. The network’s topological structure may be different, then we adopt Greedy Algorithm(GA)to find original nodes of the new network. We also analyze the controllability of Erd?s-Rényi(ER) random network, Scale-free(SF) network and Random regular(RR)network. Finally, we find that the network with immune nodes is more difficult to control, and also the immune nodes’ degree play an important role in this relationship. The greater the degree of immune nodes get, the larger the network topology changes. The proportion of the source node and the original network will be different. In other words, choose the degree of greater node as immune to isolation, so the process of looking for source node will become more complicated. Such as thespread of the virus, and the node failure in the power network, we can adopt isolation for those nodes with litter degree, which makes us relatively easier to establish a good control of target set.