# Collective movement in alarmed animals groups: a simple model with positional forces and a limited attention field

## TL;DR

This paper analyzes a model of alarmed animal groups' collective movement, revealing a phase transition between ordered and disordered states influenced by attention field angles, with implications for understanding perception ranges.

## Contribution

It introduces a detailed numerical analysis of a position-based model with limited attention fields, characterizing the phase transition and correlation behaviors.

## Key findings

- Identifies a discontinuous phase transition between ordered and disordered phases.
- Quantifies the critical point and scaling behavior of the transition.
- Shows strong short-range correlations in movement directions.

## Abstract

We perform a numerical analysis of a recent introduced model for describing collective movement in alarmed animals groups. This model, derived from a position-based interaction and a limited attention field, displays a non-equilibrium phase transition between a crystal-like phase, characterised by a single densely packed cluster of individuals, which occurs for small attention field angles, and a disordered phase, constituted of fragmented clusters, which emerges at large angles. The transition is quantitatively characterised, measuring its critical point and describing its scaling behaviour, which suggests that the nature of the transition is discontinuous. Finally, we study the correlations in the directions of motion, which show strong positive values at short distances. This fact suggests that individuals' effective perception range goes far beyond the model interaction range.