No abstract

No abstract

Rumor propagation as a typical form of social communication in online social networks has had a significant negative impact on a harmonious and stable society. With the rapid development of mobile communication equipments, traditional rumor propagation models, which depend on ordinary differential equations (ODE), may not be suitable for describing rumor propagation in an online social network. In this paper, based on reaction-diffusion equations, we propose a novel epidemic-like model with both discrete and nonlocal delays for investigating the spatial-temporal dynamics of rumor propagation. By analyzing the corresponding characteristic equations of this model, the local stability conditions of a boundary equilibrium point and a positive equilibrium point are established. By applying the linear approximation method of nonlinear systems, sufficient conditions are derived for the existence of Hopf bifurcation at the above two kinds of equilibrium points. Moreover, a sensitivity analysis method based on the density of spreading users is proposed, and then in theoretical and experimental aspect we identify some sensitive parameters in the process of rumor propagation. Finally, numerical simulations are performed to illustrate the theoretical results.

No abstract

No abstract

No abstract

Mathematical modeling is an important approach to research rumor propagation in online social networks. Most of prior work about rumor propagation either carried out empirical studies or focus on ordinary differential equation models with only consideration of temporal dimension; little attempt has been given on understanding rumor propagation over both temporal and spatial dimensions. This paper primarily addresses an issue related to how to define a spatial distance in online social networks by clustering and then proposes a partial differential equation model with a time delay to describing rumor propagation over both temporal and spatial dimensions. Theoretical analysis reveals the existence of equilibrium points, a priori bound of the solution, the local stability and the global stability of equilibrium points of our rumor propagation model. Finally, numerical simulations have analyzed the possible influence factors on rumor propagation and proved the validity of the theoretical analysis.

No abstract