Propagation of the state change induced by external forces in local interactions

This paper analyses the propagation of the state changes of agents that are induced by external forces applied to a plane. In addition, we propose two models for the behavior of the agents placed on a lattice plane, both of which are affected by local interactions. We first assume that agents are allowed to move to another site to maximise their satisfaction. Second, we utilise a model in which the agents choose activities on each site. The results show that the migration (activity) patterns of agents in both models achieve stability without any external forces. However, when we apply an impulsive external force to the state of the agents, we then observe the propagation of the changes in the agents’ states. Using simulation studies, we show the conditions for the propagation of the state changes of the agents. We also show the propagation of the state changes of the agents allocated in scale-free networks and discuss the estimation of the agents’ decisions in real state changes. Finally, we discuss the estimation of the agents’ decisions in real state temporal changes using economic and social data from Japan and the United States