Liancheng Wang, Min Wang
Department of Mathematics, Kennesaw State University, Marietta, GA, 30062, USA.
In this research, we propose and study an online social network mathematical model with delay based on two innovative assumptions:
(1) Newcomers are entering the community as either potential online network users or those who are never interested in online networks at constant rates, respectively; and
(2) It takes a certain time for the active online network users to start abandoning the network.
The basic reproduction R₀, the user-free equilibrium (UFE) P₀, and the user-prevalent equilibrium (UPE) P* are identified. The analysis of local and global stability for those equilibria is carried out. For the UPE P*, using the delay τ as the Hopf bifurcation parameter, the occurrence of Hopf bifurcation is investigated. The conditions are established that guarantee the Hopf bifurcation occurs as τ crosses the critical values. Numerical simulations are provided to illustrate the theoretical results.
Keywords: Online social network, stability, Hopf bifurcation.
Wang, L., & Wang, M. (2023). Stability and bifurcation analysis for an OSN model with delay. Advances in the Theory of Nonlinear Analysis and its Application, 7(2), 413-427.