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 in system behaviors, we demonstrate the applicability of the sigmoid curve to capture the acceleration and deceleration of growth, predicting an entitys ultimate state well in advance of reaching it. We show that our analysis can be applied to diverse systems where entities exhibit nonlinear growth using case studies of (1) customer purchasing and (2) U.S. legislation adoption. This showcases the ability to forecast months to years ahead of time, providing 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. We introduce a classification of entities based upon similar lifepaths. This study contributes to the understanding of complex system behaviors, offering a practical tool for prediction and system behavior insight that can inform strategic decision making in multiple domains.

翻译：预测动态行为是科学的普遍目标之一，也是将人类知识应用于现实世界系统诸多具体应用的关键所在。本文提出一种解析方法，利用S型增长曲线对复杂系统内个体实体的动力学行为进行建模。尽管系统行为存在非线性和不可预测性等挑战，我们证明了S型曲线在捕捉增长加速与减速过程中的适用性，能够远在实体达到最终状态之前预测其终极态势。通过(1)客户购买行为与(2)美国立法采纳两个案例研究，我们展示了该分析可应用于实体呈现非线性增长的多样化系统。这体现了提前数月乃至数年进行预测的能力，为商业领袖和政策制定者提供了宝贵洞见。此外，我们对个体组分动力学的表征提供了揭示整个系统聚合行为的框架。我们基于相似生命轨迹提出了实体分类方法。本研究深化了对复杂系统行为的理解，提供了一种可用于多领域战略决策的预测工具与系统行为洞察方法。