Impact of Individual Defection on Collective Motion

Collective motion modeling has attracted significant attention for gaining insights into the mechanisms of collective behavior and its potential to inspire control strategies for swarm robotics. Most of the existing models assume that individuals within a group strictly adhere to the interaction rules. However, individuals in artificial and natural collectives could occasionally fail to follow the interaction rules, which is distinct from noisy actions. In this study, we analyze how the presence of individuals, who occasionally defect, affects the ordered phase of the group during collective motion. Using Monte Carlo simulations, we study two collective motion models, a non-spatial (pairwise interaction) and a spatial (Couzin) model. In the non-spatial model, when individuals defect with higher probability, both the time required by the agents to reach directional consensus (polarized group motion) as well as the average energy cost of the group to maintain such directional consensus (average rotational energy consumption per individual in highly polarized groups) increases. In the spatial model, there are conditions where the presence of defecting agents can simultaneously reduce the time required by the collective to get highly polarized and the average energy cost in the polarized state. These findings not only enhance our understanding of probabilistic defective behavior in biological systems but can also inspire innovative, efficient, and controllable approaches in swarm robotics.