Knowledge transmission model with consideration of self-learning mechanism in complex networks

Based on the fact that one can attain knowledge by oneself, which is different from epidemic spreading, we analyze the knowledge transmission in complex networks. In this paper, we propose a knowledge transmission model by considering the self-learning mechanism and derive the mean-field equations that describe the dynamics of the knowledge transmission process. Furthermore, we obtain the transmission threshold R₀, which is closely related with the transmission rate and self-learning rate. Moreover, we investigate the global stability of the knowledge free equilibrium E₀ and the endemic equilibrium E* of the model. That is, when R₀ < 1, the knowledge free equilibrium point E₀ is globally asymptotically stable and the knowledge becomes completely extinct eventually; when R₀ > 1, a unique endemic equilibrium point E* is globally stable, and the knowledge can be transmitted. Finally, numerical simulations are given to illustrate the theoretical results. The simulation results indicate that the self-learning factor has an obvious promoting effect on the knowledge transmission, both in scale-free and homogeneous networks. Besides, the simulation results illustrate that the scale-free network is more efficient to knowledge transmission.