Research On Successive Faults And Controllability Of Several Types Of Complex Networks And Super Networks

With the development of present science and technology,networks are applied in various fields of modern society.Network science has been influencing the people's life and production.We had better understand for complex networks by modeling and analyzing the topological properties.While one of the ultimate goals for study-ing complex networks is to study the dynamics properties of networks.The study of the dynamics behavior can help people understand the network features more clear and solve many practical problems.Such as,eastern interconnection black-out reflects the cascading failure behavior of complex network;the signal input of complex systems can be solved by controllability of complex networks.At present the,researher on cascading failure,synchronization,controllability and spreading has become the hot point and the theme of network science.Based on complex network theory,hypergraph and hypernetwork theory,we investigate cascading failure of a class network which is closer to the reality of life,and this network is Harmonious Unification Hybrid Preferential Model.According to the characteristic of the real hypernetwork,we study the cascading failure of k uniform scale-free hypernetwork.Then we discuss the controllability of a class deterministic networks with the identical degree sequence.Moreover we construct a class deterministic hypernetworks and analyze their controllability.The main research works and contributions of this dissertation are summarized as following:(1)Analyze the cascading failure of Harmonious Unification Hybrid Preferential Model(HUHPM).We analyze the network's ability to fight random attacks and deliberate attacks and find robustness measure of HUHPM network.In addition,we give theoretical derivations of disturbance threshold which will trigger a global fault and get the approximate solutions.The correctness of the theoretical analysis is testified by comparing the theoretical and simulation results.(2)According to the diffusion pattern of cascading failure that happen in ex-press hypernetwork and electronic hypernetwork,we first propose two methods based on hyper-graph theory and analyze the characteristic of the cascading fail-ure of these two kinds of network.The cascading failure of k uniform scale-free hypernetwork is given by computer numerical simulation.The robustness and in-fluencing factors of hypernetwork are analyzed.We compare the robustness of k uniform scale-free hypernetworks with BA scale-free network and obtain some re-sults.Meanwhile,we give the approximate solutions of disturbance threshold.(3)Under the multidimensional space,we first proposed a new CML cascading failure model that are good at describing cascading failure behavior happen in k uniform hypernetworks based on hyper adjacent matrix and joint degree.Then we simulate the cascading failure process of 3 uniform hypernetwork and analyze the robustness and influencing factors.The approximate solution of disturbance threshold is derived and validated via the simulation experiment.(4)By exact controllability theory,we study the collability of a class of deter-ministic network with identical degree sequence,called(x,y)-flower.We analyze controllability of the two deterministic networks((1,3)-flower and(2,2)-flower)in detail and give accurate results of the minimum number of driver nodes for the two networks.Moreover,we develop the(1,3)-flower network and propose a de-terministic hypernetwork model:2k uniform hyper(1,3)-flower network.We first construct the deterministic hypernetwork and analyze its controllability using the hypergraph theory and exact controllability theory.