Bifurcation and control of a delayed diffusive logistic model in online social networks

Online social networks have become a popular source for disseminating information and facilitating the building of social relations among a huge number of people. Recently, several partial differential equations were proposed to model the spatio-temporal dynamics of information diffusion in online social networks. As a result, mathematical results of reaction-diffusion equations can be used to help understand the mechanism of information diffusion and, in particular, increase the efficiency of distributing positive information while reducing unwanted information. In this paper, we develop a Partial Differential Equation (PDE) with a delayed feedback controller to effectively control the spread of harmful information. Applying the theory of partial function differential equation, we present verifiable control conditions for stability and Hopf bifurcation of the feedback control system. Examples are given to demonstrate that the delayed feedback controller can reduce the density of influenced users effectively and delay the onset of Hopf bifurcation as well.