Oscillator Chain Model for Multi-Contour Systems With Priority in Conflict Resolution

Synchroinfo Journal. 2025. Vol. 11. No. 1. P. 34–40.

Lubashevsky I., Yashina M., Lubashevskiy V.

We propose a novel model of oscillatory chains that generalizes the contour discrete model of Buslaev nets. The model offers a continuous description of conflicts in system dynamics, interpreted as interactions between neighboring  oscillators when their phases lie within defined interaction sectors. The size of the interaction sector can be seen as a measure of vehicle density within clusters moving along contours. The model assumes that oscillators can synchronize their dynamics, using concepts inherited from the Kuramoto model, which effectively accounts for the discrete state effects observed in Buslaev nets. The governing equation for oscillator dynamics incorporates four key factors: deceleration caused by conflicts with neighboring oscillators and the synchronization process, which induces additional acceleration or deceleration. Numerical analysis shows that the system exhibits both familiar properties from classic Buslaev nets, such as metastable synchronization, and novel behaviors, including phase transitions as the interaction sector size changes.

Keywords: синхронизация, phase transitions, фазовые переходы, chain of oscillators, synchronization, транспортные модели, Buslaev nets, traffic model, сети Буслаева