A Dynamic Complex Network Model Of The Mobile Ad Hoc Communication Network

In the past few years, the study of complex network has attracted a lot of interest of physicists. Complex networks can describe a variety of different practical systems. Complex systems are investigated by the complex networks in which the units of systems are modeled as nodes and the interactions among them are modeled as edges between these nodes. Physicists have done many researches on the structure and dynamics on static complex networks. Now we choose to discuss the self-organized dynamic complex networks and dynamics on it on the basis of former works.The method of complex networks is used to study a new dynamic communication network——mobile ad hoc communication network in the present thesis. Considering particular characteristics of it,first we study the connectivity of the mobile ad hoc communication network on a two-dimensional triangular lattice and a square lattice. Scaling behavior of global connectivity is found out. It serves a sort of site percolation on dynamic complex networks relative to the geometric distance. Moreover, we calculate parameters of complex network of mobile ad hoc network when it is globally connected. The result reveals the property of dynamic small world network at critical points. Therefore, we continue to study the dynamic small world network model of mobile ad hoc networks, and find out the analytical solution to the rewiring probability of the network as a function of the velocity and the transmission range of nodes. Then, the simple model of such a dynamic network is used to study the problem of information communication and other dynamics on the mobile ad hoc communication network. At last, we study the epidemics of it. Taking the worm epidemics as an example, we study the property of epidemic spreading process on a two dimensional triangular lattice and two-dimensional dynamic small world network, respectively. It is found that not only transmission threshold is enhanced but also the epidemic prevalence is reduced obviously. Moreover, a universal function describing the ratio of immune nodes in the dynamical small-world network is obtained by rescaling the time with the rewiring probability of it.Starting from real observables of the mobile ad hoc communication network, we set up new kind of models of dynamical complex networks pertaining to geometric distance, which yields important potential applications and serves a practical background for the percolation problem in complex networks. Results of a few scaling functions are new progress not seen previously. In addition, the MAC mechanism can become a sort of new problems in statistical physics, and manifest its creative theoretical significance in the future.