Maintaining cohesion between randomly moving agents in unbounded space is an essential functionality for many real-world applications requiring distributed multi-agent systems. We develop a bio-inspired collective movement model in 1D unbounded space to ensure such functionality. Using an internal agent belief to estimate the mesoscopic state of the system, agent motion is coupled to a dynamically self-generated social ranking variable. This coupling between social information and individual movement is exploited to induce spatial self-sorting and produces an adaptive, group-relative coordinate system that stabilises random motion in unbounded space. We investigate the state-space of the model in terms of its key control parameters and find two separate regimes for the system to attain dynamical cohesive states, including a Partial Sensing regime in which the system self-selects nearest-neighbour distances so as to ensure a near-constant mean number of sensed neighbours. Overall, our approach constitutes a novel theoretical development in models of collective movement, as it considers agents who make decisions based on internal representations of their social environment that explicitly take into account spatial variation in a dynamic internal variable.
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