Complex Network Stability Study

This thesis is concerned with the study of the dynamics stability of complex network driven by non-equilibrium fluctuation and virus's spreading mechanism on complex network under the intentional attack, which use the non-equilibrium statistical theory, the stochastic differential equation method as well as the Fokker-Plank equation steady-state solution. These studies are very important both in theory and in practical applications. By studying stability of complex network, on the one hand, we can understand and explain the dynamic properties presented in real-world networks; and on the other hand, we can apply these theoretical results of complex network stability to some practical applications, for instance, we may design of real network to achieve a better performance by using this results. By studying virus's spreading mechanism on complex network under the intentional attack, on the one hand, we can provide the rationale to study and develop the new immunity mechanism and the strategy; on the other hand, there are advantageous in raising the network transmission effection. In addition, complex network theory more and more widespread applies in many domains. As this topic main contents, we summarized the application of complex network theory in the electronic circuit and microelectronics.The main contents and originalities in this thesis can be summarized as follows:1. Non-equilibrium fluctuation and small-world network stabilityUsing the non-equilibrium statistical theory, the stochastic differential equation method as well as the Fokker-Plank equation steady-state solution, we have studied the small-world network stability by abstracting the real network factors of element mistake, node breakdown and so on as the non-equilibrium stochastic fluctuation. We discuss separately two kinds of situations to unify structure parameters of small-world network model, one is the fluctuation to occur in the non-linearity affects the coefficient and another is in the NW length scale.(1)Through fundamental research, our initial find out: if the non-equilibrium fluctuation occurs in the NW length scaleζ, the NW length scale's mean value rapid growth driven by fluctuationσ~2. It implies that randomization connection probability p is invariable; the complex network degree's value k will be rapidly reduced. When k reduces to some value (for instance: k< 1), the stability of complex network system structure will have a fierce change. May know by the NW length scaleζdefinition, the complex network node should still exist, but the connection between the nodes is deleted completely. This kind of situation might correspond in the entire complex network system collapse. This conclusion full explains that the NW length scaleζis a primary factor to decide the dissemination stable as the small-world network characteristic parameter. When it appears fluctuation and approach a certain threshold, the complex network stability and the macroscopic dynamics behavior will have the fierce change, until will appear the entire net collapse. It is revealed that the NW length scaleζis one of extremely sensitive factors in the complex network dynamics process.(2)Comparatively, if the non-linearity mutually coefficient A, has the non-equibirum fluctuation, the NW length scaleζalong with the fluctuationσ~2 has the tendency to drop rapidly. if randomisation connection probability p is invariable, complex network degree k can increase slowly. These phenomenons show the network system connectivity strongly and complex network can develop to a stabler direction. It is to say, if the fluctuation occurs in the system non-linear mutually coefficient, it can not lead to the complex network system stability to sudden change.2. Intentional attacks and complex network stabilityPerhaps intentional attacks have many ways, but virus attacks on network are like this being in flood, we have to take it seriously.(1) We proposed one kind of new model SIS-BD model which represent virus dissemination. Using this model and non-equibirum statistical theory as well as stochastic process theory and method, we study the virus spreading from three aspects: earlier period, the later period and the dissemination entire process. We get the virus infection density function distributed rule of virus spreading in three periods. To compare with the actual data, we know that this distribution function accord with the actual data well.(2) In the research process we discovered virus's effective dissemination speed is not a constant, it is a kind of function which can describe a similar Logistic differential equation. It is obvious different in the traditional infectious disease studies in which virus's dissemination speed is usually a constant. By solution the similar Logistic differential equation and useing the actual data fiting the correlation constant, and union two part of findings, we obtain the infection density distribution function of virus spreading on entire process.(3) By further analyzes the effective dissemination speed we know that it close correlate with network structure parameter. Therefor, we used the theoretical analysis the method to discuss the effective dissemination speed and the complex network architecture parameter relation. Finally, we get the virus dissemination effective speed to relate with the network architecture parameter more general function.3. Non-equilibrium statistical theory and methodIt is one kind of innovation technique that uses the non-equilibrium statistical theory and method to research complex network.Finally, we discussed the application of complex network theory in the electronic circuit and microelectronics. First, we introduce the main application and achievement of complex network on electronic circuit. Second, we make to a brief report about the complex network application in the quantum coherent network and nanometer wire nets, which become the newest research hot spot and attract to how widespread research interest at present.