[Paper Review] Anticipation induces polarized collective motion in attraction based models

Daniel Strömbom, Alice Antia|arXiv (Cornell University)|Oct 16, 2017

Distributed Control Multi-Agent Systems18 references3 citations

TL;DR

This paper demonstrates that anticipation—using future positions of neighbors—induces polarized collective motion in a synchronous, off-lattice, attraction-only model of self-propelled particles, contrary to prior findings that anticipation suppresses polarization in alignment-based models. The key result is that anticipation acts as a direct mechanism for polarization, enabling coherent group formation where none existed without it.

ABSTRACT

In most models of collective motion in animal groups each individual updates its heading based on the current positions and headings of its neighbors. Several authors have investigated the effects of including anticipation into models of this type, and have found that anticipation inhibits polarized collective motion in alignment based models and promotes milling and swarming in the one attraction-repulsion model studied. However, it was recently reported that polarized collective motion does emerge in an alignment based asynchronous lattice model with mutual anticipation. To our knowledge this is the only reported case where polarized collective motion has been observed in a model with anticipation. Here we show that including anticipation induces polarized collective motion in a synchronous, off lattice, attraction based model. This establishes that neither asynchrony, mutual anticipation nor motion restricted to a lattice environment are strict requirements for anticipation to promote polarized collective motion. In addition, unlike alignment based models the attraction based model used here does not produce any type of polarized collective motion in the absence of anticipation. Here anticipation is a direct polarization inducing mechanism. We believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.

Motivation & Objective

• To investigate whether anticipation can induce polarized collective motion in a synchronous, off-lattice, attraction-based model.
• To determine if asynchrony, lattice constraints, or mutual anticipation are necessary for anticipation to promote polarization.
• To clarify whether anticipation stabilizes, promotes, or inhibits milling and swarming in attraction-only models.
• To explore the generality of anticipation as a mechanism for polarization across different collective motion models.

Proposed method

• A synchronous, off-lattice self-propelled particle model is used, where particles update positions and headings simultaneously at each time step.
• Each particle calculates the local center of mass (LCM) of neighbors within a radius R using current positions in the baseline model.
• In the anticipation variant, particles use the anticipated future positions of neighbors—projected forward by δ distance along current heading—to determine neighbor inclusion for LCM calculation.
• The new heading is computed as a linear combination of the normalized direction to the LCM and the current heading, with weight c.
• Simulations are run across a range of c values (0.04 to 2.0) to map group type transitions.
• Polarization and group size are quantified using α (polarization measure) and σ (scaled size), with results averaged over 100 simulations.

Experimental results

Research questions

• RQ1 Does anticipation induce polarized collective motion in a synchronous, off-lattice, attraction-only model?
• RQ2 Is asynchrony, lattice restriction, or mutual anticipation required for anticipation to promote polarization?
• RQ3 How does anticipation affect the formation of mills and swarms in attraction-based models?
• RQ4 Can anticipation serve as a direct mechanism for polarization in models without explicit alignment terms?
• RQ5 Is the effect of anticipation on collective motion consistent across different model architectures?

Key findings

• Anticipation induces polarized collective motion in a synchronous, off-lattice, attraction-only model, which otherwise produces only mills and swarms.
• A sharp transition in polarization occurs at c ≈ 1.25, where cohesive polarized groups emerge where no group forms without anticipation.
• Swarm formation is inhibited by anticipation, with polarization increasing and swarm size decreasing as c increases.
• The mill regime is partially destabilized by anticipation, with smaller mills being replaced by polarized groups.
• The model shows that neither asynchrony, lattice constraints, nor mutual anticipation are necessary for anticipation to promote polarization.
• The results suggest anticipation is a general and underutilized mechanism for generating polarized motion in collective systems.