Reseach On Explosive Percolation And The Spread Of Epidemic In The Complex Networks

Percolation is one process on which statistical physics and mathematics has widely research, and it was also an important tool to analysis the spread of epidemic, and the information transmission. For a long time, it was considered that the evolution of random network would undergo a continuous second order phase transition. Achlioptas reported that the process(AP) under random network percolation transform has an amazing mutation phenomenon, and they called this phenomenon “explosive percolation”. In recent years, the explosion percolation has triggered a lot of theory and simulation works and its application in the real complex networks.In this paper, we have done the following two works according to the relative reasearch:(1) A modifed BFW percolation model was proposed by changing the way of selecting candidate edges. Through numerical simulations, we find that the generated network structure depends on the model parameter q, which controls the probability of adopting preferential attachment in choosing candidate edges. Without loss of generality, we consider the network structure when the number of edges is 1.5 times of the system size. With the increase of q, the network degree distribution changes from Poission to power-law. Moreover, our study indicates that there exists a critical value cq, above which the modifed BFW model undergos multiple random transitions in the supercritical region. Otherwise, only one first-order transition exists. Additionally, we also find a critical point cq? of the transition type. Simulation results show that the discontinuous transition becomes continuous when q exceeds cq?.(2) Based on the SIS model,we study the disease spreading,and made a research of resource allocation problem, using mean field theory, the dynamic propagation equation was established. And according to the initial efficiency of the disease spreading 0q, the initial ratio of infected nodes ??0? and the coefficient of investment of resources R, and we discussed the final number of infected rate along with the change of coefficient of resource R.Through the regular network, ER network and power law networks numerical simulation on the network and the equation we found that with given disease transmission efficiency 0q, there exists first transition in the evolution process of the infected ridio with R. And we find the relationship of the transition point and the initial rido of the infected nodes.The above results will have very important application value for the prevention and the controlling of the spread of the disease or harmful information.