This paper studies how scale-free correlations, a key feature for efficient group
response, emerge in collective motion under communication energy constraints. A
two-dimensional Boids model integrated with a point-to-point wireless
communication energy consumption model is used. The model dynamically
determines, based on a limited communication power budget, an individual’s
interactive neighbors, where neighbors are selected based on two different
mechanisms: distance-based and probability-based, until the total communication
cost reaches the budget. Simulations of flock sizes ranging from 30 to 230
individuals confirm that scale-free correlation persists, even under strict
power constraints, which is shown by a correlation length ξ proportional to the
flock’s linear size L. Notably, the ratio ξ/L, which reflects the robustness of
collective correlation, displays a non-monotonic dependence on the available
communication power. Initially, increasing power enhances ξ/L by expanding
effective interaction ranges and improving information transmission. However,
beyond a threshold, further power increase causes a slow drop in ξ/L, likely due
to signal interference from excessively many or distant connections. This
finding demonstrates that communication power is a critical, tunable engineering
parameter regulating collective coordination, analogous to interaction range or
neighbor number in biological models. The results imply that for engineered
swarms, maximizing communication resources is not always beneficial; instead, an
optimal power allocation exists to maximize coordination performance, balancing
connectivity with efficient, localized interactions.