Bifurcation Analysis In A Continuous-Time Information Model With Discrete And Distributed Delays

In this paper, we consider a continuous model with discrete and distributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each equilibrium. Taking time delay as a bifurcation parameter, the system undergoes a sequence of Hopf bifurcation when this parameter passes through a critical value. By methods of multiple scales, we prove that the direction of Hopf bifurcation is closely related to delay and numerical simulation also illustrate the results. Finally, the simulation show the sensitivity of delay and we give the control strategy which is important to application.