Noise effects in Schelling metapopulation model with underlying star topology

The Schelling model, one of the most famous agent-based models in social physics, describes the formation of social segregated groups of agents based on their preferences. It has received significant attention, and various versions of the model have been extensively developed and studied as well. In this paper, we examine the impact of noise on Schelling’s metapopulation segregation model, specifically focusing on an underlying star topological structure. Our findings demonstrate that the fascinating effects caused by the star topology become fragile when the model is subjected to noise. We conducted theoretical analyses and numerical simulations to investigate the stationary state of the systems, their evolutionary process, and the distribution of the agents. Our results indicate that the anomaly in optimizing collective utility by egoists diminishes at a non-vanishing level of noise. On the other hand, altruists regain their ability to optimize collective utility. As the noise level increases, the resulting randomness becomes dominant in the movement of agents, leading to a reduced distinction between the two types of agents and eventually become random walkers. Graphical abstract The intriguing effects of Schelling’s metapopulation segregation model with underlying star topology become fragile when noise parameter is introduced.