Fig. 3: Individual information acquisition.
From: Allocentric flocking
A–F The network activity as a function of time (i) and the resulting trajectories (ii) for egocentric and allocentric representations for increasing values of β is shown. For too small β, for both egocentric and allocentric representations of space, the agent only exhibits random and slow movement. Above the order-disorder transition, the agent moves towards the target. For smaller values of β, noise drives transitions between states, which facilitate information acquisition by endowing the agent with flexibility. In the ordered phase, external stimuli elicit distinct network activities for allocentric and egocentric representations of space. With an allocentric representation, external stimuli can lead to the formation of damped traveling waves corresponding to spiral motion toward the target (with more stability for larger values of β). For too large β, trajectories intermittently veer away from the target. With an egocentric representation, external stimuli help stabilize a bump of activity, allowing agents to remain stationary once it has found the target. G The agent’s decision-making time in finding a stationary target, defined as the time needed for the agent to reach close proximity of the target (5 dimensionless units), is plotted as a function of β. Decision-making time is minimized in the ordered phase. An allocentric representation can improve the decision-making speed in the effective decision-making region. H, I The time average distance of the agent to the target, normalized by the arena size L = 1000, d/L, as a function of β for both allocentric and egocentric representations and for different target speeds, is plotted. For a stationary or slowly moving target, an egocentric representation is beneficial by allowing the agent to stay stationary once it finds the target. However, for larger target speeds, an allocentric representation improves information acquisition by facilitating the tracking of a rapidly moving target. In both cases, the information acquisition optimizes in the ordered phase but is close to the critical point. Parameter values: v0 = 10, σ = 2π/Ns, L = 1000, h0 = 0.0025, and hb = 0. A–F Ns = 100, and in G–I Ns = 400.
