Predicting system dynamics of pervasive growth patterns in complex systems.

Predicting dynamic behaviors is one of the goals of science in general as well as essential to many specific applications of human knowledge to real world systems. Here, we introduce an analytic approach using the sigmoid growth curve to model the dynamics of individual entities within complex systems. Despite the challenges posed by nonlinearity and unpredictability, we demonstrate that sigmoid-like trajectories frequently emerge in systems where entities undergo phases of acceleration and deceleration of growth. Through case studies of (1) customer purchasing behavior and (2) U.S. legislation adoption, we show that these patterns can be identified and used to predict an entity's ultimate state well in advance of reaching it. This provides valuable insights for business leaders and policymakers. Moreover, our characterization of individual component dynamics offers a framework to reveal the aggregate behavior of the entire system. Moreover, our classification of entity lifepaths contributes to understanding system-level structure by revealing how individual-level dynamics scale to aggregate behaviors. This study offers a practical modeling framework that captures commonly observed growth dynamics in diverse complex systems and supports predictive decision-making.