Stability and Bifurcation Analysis For An OSN Model with Delay

Authors : Liancheng WANG, Min WANG

Pages : 413-427

Doi:10.31197/atnaa.1152602

View : 35 | Download : 36

Publication Date : 2023-07-23

Article Type : Research Paper

Abstract :In this research, we propose and study an online social network mathematical model with delay based on two innovative assumptions: insert ignore into journalissuearticles values(1); newcomers are entering community as either potential online network users or that who are never interested in online network at constant rates, respectively; and insert ignore into journalissuearticles values(2); it takes a certain time for the active online network users to start abandoning the network. The basic reproduction $R_0,$ the user-free equilibriuminsert ignore into journalissuearticles values(UFE); $P_0,$ and the user-prevailing equilibriuminsert ignore into journalissuearticles values(UPE); $P^*$ are identified. The analysis of local and global stability for those equilibria is carried out. For the UPE $P^*,$ using the delay $\\tau$ as the Hopf bifurcation parameter, the occurrence of Hopf bifurcation is investigated. The conditions are established that guarantee the Hopf bifurcation occurs as $\\tau$ crosses the critical values. Numerical simulations are provided to illustrate the theoretical results.
Keywords : Online social network, stability, Hopf bifurcation