Bifurcation Analysis in a Continuous-Time Information Model with   Discrete and Distributed Delays
  In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each e-quilibrium. 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 depending on the condition which is related to delay. 
Jingli Ren and Fangzhi Yu
math.DS