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Modeling of knowledge transmission by considering the level of forgetfulness in complex networks. (English) Zbl 1400.34090

Summary: In this study, we establish a general model by considering the level of forgetfulness during knowledge transmission in complex networks, where the level of forgetfulness depends mainly on the number in a crowd who possess knowledge, while the saturated incidence is also considered. In theory, we analyze the stability of the equilibrium points and the transmission threshold \(R_0\) is also given. If \(R_0 > 1\), then knowledge can be transmitted, but if not, it will become completely extinct. In addition, we performed some numerical simulations to verify the reasonability of the theoretical analysis. The results of the simulations also suggest that the proportion of the crowd with knowledge will be increased under a better cultural atmosphere.

MSC:

34D20 Stability of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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