Research on the Dynamics Model for Microblog Information Dissemination Based on Forwarding
Micro-blog, the new type of mobile information service mode, using the fully in-tegrated between wired and wireless networks, bringing into instant messaging plat-form of social relationships, which has the characteristics of disseminating and inter-acting information in anytime and anywhere. Micro-blog dramatically changes the way of information transmission. The development of micro-blog is regarded as a rev-olutionary innovation with a unique propagation mode. This paper mainly discusses information spread in the real world through micro-blog network in detail, which lays the transmission mechanism and propagation characteristics, and determines the in-fluence of information. The detail researches are as follows.Firstly, the characteristics of information dissemination in micro-blog network are analyzed, and the similarity between micro-blog forwarding and random walk are compared. We present the thought of using the frame of random walk to study the micro-blog information spread in the real world.Secondly, the statistical properties of forwarding time and displacement are ana-lyzed in detail based on the actual forwarding data of popular micro-blogging. We find that forwarding time obeys nonhomogeneous Poisson distribution, forwarding time interval and displacement have power law tail. The power law tail of forwarding time interval slows down the information spread in space and makes sub-diffusion of the information spread, meanwhile, the power law tail of forward displacement speeds up the information spread in space and makes super-diffusion of information diffusion.Then based on the definition and characteristics of fractional derivative, we con-struct the mathematic model-bifractional derivative anomalous diffusion model to describe the antagonistic interplay between forwarding displacements and forward-ing time interval using the frame of continue time random walk. A bridge between micro-blog information dissemination and anomalous diffusion theory is built by con-structing the anomalous diffusion model.Using the model to study micro-blog information spread, the theoretical analy- sis and numerical solution of the model are very important. However, the numerical methods and theoretical analysis to the bifractional anomalous diffusion model are very difficult due to the memory effect of the fractional derivative.The second part focuses on the numerical solution of the fractional anomalous dif-fusion model, and proposes two numerical methods. The main contributions are as follows.Chapter 4 presents cubic B-spline wavelet collocation method to solve fractional anomalous diffusion model. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are proposed, and the problem is converted into a system of algebraic equations which is suitable for computer programming. It over-comes the difficulty in numerically solving fractional anomalous diffusion model due to the memory effect of fractional derivative. Compared with time marching method, error of wavelet collocation method accumulates much slower with time and is almost uniformly distributed. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.Since the calculation for the unknown function in the differential equation is con-verted into those of cubic B-spline wavelet basis functions in wavelet collocation method, the order of the fractional differential equation is limited. Furthermore, the derivative operation to the unknown function is written in the linear combination of wavelet basis function’s corresponding operation, which will reduce the precision of the solution.To overcome the limitation of wavelet collocation method, we propose the cubic B-spline operational method to solve fractional differential equation in chapter 5. We construct the cubic B-spline operational matrix of fractional derivative in the Caputo sense, and fractional differential equation is converted into a system of algebraic equa-tions. Numerical results demonstrate that the method is good in terms of accuracy.