Cognitive decision-making processes are crucial aspects of human behavior, influencing various personal and professional domains. This research delves into the application of differential equations in analyzing decision-making accuracy by leveraging eye-tracking data within a virtual industrial town setting. The study unveils a systematic approach to transforming raw data into a differential equation, essential for deciphering the relationship between eye movements during decision-making processes. Mathematical relationship extraction and variable-parameter definition pave the way for deriving a differential equation that encapsulates the growth of fixations on characters. The key factors in this equation encompass the fixation rate $(\lambda)$ and separation rate $(\mu)$, reflecting user interaction dynamics and their impact on decision-making complexities tied to user engagement with virtual characters. For a comprehensive grasp of decision dynamics, solving this differential equation requires initial fixation counts, fixation rate, and separation rate. The formulation of differential equations incorporates various considerations such as engagement duration, character-player distance, relative speed, and character attributes, enabling the representation of fixation changes, speed dynamics, distance variations, and the effects of character attributes. This comprehensive analysis not only enhances our comprehension of decision-making processes but also provides a foundational framework for predictive modeling and data-driven insights for future research and applications in cognitive science and virtual reality environments.

翻译：认知决策过程是人类行为的关键环节，深刻影响着个人与专业领域的诸多层面。本研究依托虚拟工业城镇环境中的眼动追踪数据，深入探究微分方程在分析决策准确性中的应用。研究提出了一种系统方法，将原始数据转化为微分方程，以揭示决策过程中眼动模式的关键关联。通过数学关系提取与变量参数定义，推导出描述角色注视增长过程的微分方程。该方程的核心参数包括注视率（λ）和分离率（μ），分别反映用户交互动态及其对决策复杂性的影响——这种复杂性源于用户与虚拟角色的互动强度。为全面把握决策动态，求解该微分方程需已知初始注视次数、注视率与分离率。微分方程的构建融合了互动持续时间、角色-玩家距离、相对速度及角色属性等多重因素，从而实现对注视变化、速度动态、距离演变及角色属性效应的量化表征。该综合分析不仅深化了对决策过程的理解，更为认知科学与虚拟现实环境中的预测建模及数据驱动研究提供了基础框架，助力未来相关领域的探索与应用。