Fig. 7: Collective behavior in large groups of agents with allocentric representation of space.
From: Allocentric flocking
A, B The distribution of GO (AOP) and LO (normalized topological VOP) in groups of various sizes of agents with an allocentric representation of space close to the order-disorder transition (A) and close to the collective motion-aggregation phase transition (B). Both phase transitions tend to a continuous phase transition, indicated by large fluctuations and a broad distribution of the order parameter, as group size increases. C, D Global order (GO) and mean distance between all pairs normalized by space size, L, as a function of time for different values of total social attraction are plotted. The system shows intermittency between high and low orders resulting from transitions between different motion patterns and strong fission-fusion dynamics. E–G Example snapshots of motion patterns from the Supplementary Videos for some values of \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\) shown in A, B. In the collective motion phase, the system shows a rich set of motion patterns, including flocking (E), sudden direction change and fission-fusion dynamics (F), and intermittency between highly ordered motion and aggregation leading to explosive movement with low local order (G). Parameter values: Ns = 100, v0 = 10, hb = 0, σ = 2π/Ns, β = 400, N = 320, and L = 1000.
