Kuramoto Synchronization in LLM-Based Multi-Agent Systems

Large language models are increasingly used as cognitive engines for autonomous agents, making it important to understand whether collective behaviours can emerge when multiple agents interact. In this work, we investigate spontaneous synchronization in a simple system of LLM-based agents moving in a one-dimensional circular environment. At each time step, agents receive local information about neighbouring agents and use an LLM to select their next movement speed. We test four different LLMs and vary the number of observed neighbours to study how information availability affects collective behaviour. Synchronization is measured using the Kuramoto order parameter, and a classical Kuramoto model is fitted to the observed trajectories. Results show that spontaneous synchronization emerges across all tested LLMs, despite substantial differences in their individual movement behaviour. The amount of local information strongly affects both the level and the temporal stability of synchronization: intermediate information produces stronger synchronization, while richer information leads to weaker but more persistent and less irregular collective states. The Kuramoto fitting supports this interpretation by showing stronger effective coupling when agents observe larger neighbourhoods. These results suggest that collective coordination can emerge in LLM-based multi-agent systems even without explicit synchronization instructions, with potential implications for their analysis, monitoring, and control.