标题： 循环交通系统中振荡动力学的数学建模 显示英文标题

标题： Mathematical Modelling of Oscillatory Dynamics in Circular Traffic Systems

摘要： 本文提出了一种关于环形轨道上交通动力学的严格分析模型，展示了由于微观驾驶员行为、延迟响应和接近压力而产生的驻波振荡的出现。 无需依赖仿真，我们推导了一系列耦合的时滞微分方程来模拟车辆之间的相互作用。 通过引入基于记忆的符号系统，我们建立了一个包含随机初始条件、非均匀反应时间和认知延迟的数学框架。 我们使用傅里叶分解和模态扰动技术进行了全面的线性稳定性分析。 我们的结果确定了谐波感应的关键阈值，界定了安全跟车距离的范围，并揭示了驾驶员过度修正的滞后现象。 分析最后讨论了对自动驾驶车辆控制的含义以及抑制振荡不稳定的潜在策略。 所有推导都是纯符号性的，并且经过了严格的数学证明。 显示英文摘要

摘要： This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without relying on simulation, we derive a series of coupled delay differential equations to model vehicular interactions. By introducing a mnemonic-based symbolic system, we establish a mathematical framework incorporating stochastic initial conditions, non-uniform reaction times, and cognitive lag. A full linear stability analysis is conducted using Fourier decomposition and modal perturbation techniques. Our results identify critical thresholds for harmonic induction, delineate the bounds of safe following distances, and reveal hysteresis in driver overcorrection. The analysis concludes with implications for autonomous vehicle control and potential suppression strategies for oscillatory instability. All derivations are purely symbolic and analytically proven.