TY - JOUR T1 - Stability and Bifurcation Analysis For An OSN Model with Delay AU - Wang, Liancheng AU - Wang, Min PY - 2023 DA - July DO - 10.31197/atnaa.1152602 JF - Advances in the Theory of Nonlinear Analysis and its Application JO - ATNAA PB - Erdal KARAPINAR WT - DergiPark SN - 2587-2648 SP - 413 EP - 427 VL - 7 IS - 2 LA - en AB - In this research, we propose and study an online social network mathematical model with delay based on two innovative assumptions: (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 (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 equilibrium(UFE) $P_0,$ and the user-prevailing 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 $\tau$ 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. KW - Online social network KW - stability KW - Hopf bifurcation CR - [1] L. M. Bettencourt, A. Cintrn-Arias, D. I. Kaiser, and C. Castillo-Chvez, The power of a good idea: quatitative modeling of the spread of ideas from epidemiological models, Physica A: Statistical Mechanics and its Applications, 364 (2006), 513–536. CR - [2] J. Cannarella and J. Spechler, Epidemiological modeling of online network dynamics, arXiv preprint arXiv:1401.4208 (2014), 1–10. CR - [3] R. Chen and L. Kong and M. Wang, Stability analysis of an online social network model with infectious recovery dynamics, Rocky Mt. J. Math., accepted. CR - [4] G. Dai, R. Ma, H. Wang, F. Wang, and K. 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