Research On Percolation Transition In The Complex Networks

Complex networks are everywhere in human’s lives,such as people transport goods through express network and communicate with each other through communication network and so on.Complex networks have become a new tool for people to understand the world.Percolation,one of basic concepts of statistical physics,is an interdisciplinary subject in the fields of statistical physics,mathematics and computer science.It is also an important research direction of complex networks.It is better to help people understand and solve problems by transforming realistic problems into network models and using complex networks percolation theory to solve them.Based on the study in various fields,we have done the following research:The influence of initial conditions on percolation.We investigate a modified ER percolation process based on classical ER percolation process,in which the initial size distribution is set to exponential distribution.Through the analysis of Smoluchowski equation,the theoretical values of order parameter,the size distribution of clusters and susceptibility are obtained.It is found that the theoretical value of order parameter is in good agreement with the experimental value near the critical point,the size distributions of clusters do not comply with the power-of distributions near the critical point and the susceptibility does not satisfy the Curie-Weiss at the critical point.We propose a modified model called restricted l-vertices based on the restricted model and the generalized triangle rules.It is found that with the increase of control parameter q,the order parameter jumps from single discontinuous jumping to multiple discontinuous jumping under the finite scale scale.Based on the theory of combinatorial mathematics,probability theory and differential equation,we explain the causes of this phenomenon,and the reasons for this phenomenon are still to be further investigated.Research on the critical resource of epidemic disease transmission.Based on the SIS model,we discuss the final infected ratio along with the resource and the existence of hysteresis loop is found.The study of the critical resources of disease control helps the government to make more reasonable decisions on disease.