Anticipation Induces Polarized Collective Motion in Attraction Based Models

Abstract

Moving animal groups are prime examples of natural complex systems. In most models of such systems each individual updates its heading based on the current positions and headings of its neighbors. However, recently, a number of models where the heading update instead is based on the future anticipated positions/headings of the neighbors have been published. Collectively these studies have established that including anticipation may have drastically different effects in different models. In particular, anticipation inhibits polarization in alignment-based models and in one alignment-free model, but promotes polarization in another alignment-free model. Indicating that our understanding of how anticipation affects the behavior of alignment-free models is incomplete. Given that attraction is a component of many alignment-free models we include anticipation in an attraction only model here to investigate. We establish that anticipation induces polarized collective motion and inhibits swarming and milling in combination with attraction alone. We also show that anticipation orients milling groups when attraction is sufficiently strong, but not otherwise. Finally, we derive an explicit heading update formula for this model with anticipation that allows for a simple heuristic explanation of its polarization inducing capacity. Due to the biological plausibility of both attraction and anticipation we believe that utilizing these components to explain collective motion in animal groups may be advantageous in some cases.