Modeling and Analysis of Delayed Matthew Effect in Social Systems via $k$-Winners-Take-All Network

A new time-delayed Matthew effect model is developed in this paper, aiming to depict the Matthew effect in social systems. Based on the construction of a social network with information transmission delay, the development speed and development potential of each agent in the social network are defined as some specific parameters, and these parameters are used to describe the status and evolutionary trend of each agent. Furthermore, this paper theoretically derives the value of the maximum time delay allowed by the proposed time-delayed Matthew effect model in a social network and verifies its convergence. Through a series of simulations, the correctness and feasibility of the proposed model are demonstrated. This work takes the time delay in information transmission into account in the Matthew effect model for the first time so that the model is capable of describing this social phenomenon accurately.