Open Access

  

Original research article

Stability and Bifurcation Analysis For An OSN Model with Delay

Author(s):

Liancheng Wang, Min Wang

Department of Mathematics, Kennesaw State University, Marietta, GA, 30062, USA.

Advances in the Theory of Nonlinear Analysis and its Applications 7(2), 413-427.
Received: August 1, 2022

  

  

  

Accepted: May 27, 2023

  

Published: June 14, 2023

Abstract

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.

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APA Style

Wang, L., & Wang, M. (2023). Stability and bifurcation analysis for an OSN model with delay. Advances in the Theory of Nonlinear Analysis and its Application7(2), 413-427.