Fig. 4: Collective behavior of agents with egocentric and allocentric representation of space.
From: Allocentric flocking
A, B Global order (GO in A), defined as the angular order parameter (AOP), and Local Order (LO in B), defined as the topological vectorial order parameter (VOP), in groups of 80 agents with an egocentric representation of space are color plotted as a function of the network inverse temperature, β, and total social attraction, \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\). For a too small social attraction, the agents move independently. As the social attraction increases, local order increases but not global order, indicating the onset of an aggregation phase where agents aggregate in a stationary dense group. C, D The global (C) and local (D) order in groups of 80 agents with allocentric representation of space as a function of the network inverse temperature, β, and total social attraction, \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\), are color plotted. The system shows three distinct phases: disordered motion for small \({h}_{{{{\rm{t}}}}}^{{{{\rm{s}}}}}\), collective motion with high local and global order, and aggregation phase with low global but high local order. Local order is minimized close to the phase transition between collective motion and aggregation due to the strong fission-fusion dynamics leading to explosive movement of the densely packed group. Parameter values: Ns = 100, v0 = 10, σ = 2π/Ns, hb = 0, N = 80, and L = 1000.
