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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.06702 |
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| _version_ | 1866909681414307840 |
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| author | Wright, Craig S |
| author_facet | Wright, Craig S |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mathematical Modelling of Oscillatory Dynamics in Circular Traffic Systems Wright, Craig S Adaptation and Self-Organizing Systems Systems and Control Dynamical Systems Optimization and Control Physics and Society 34K20, 90B20, 35B35 G.1.10; I.6.1; J.7 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. |
| title | Mathematical Modelling of Oscillatory Dynamics in Circular Traffic Systems |
| topic | Adaptation and Self-Organizing Systems Systems and Control Dynamical Systems Optimization and Control Physics and Society 34K20, 90B20, 35B35 G.1.10; I.6.1; J.7 |
| url | https://arxiv.org/abs/2507.06702 |