# Voronoi diagrams and Delaunay triangulation for modelling animal territorial behaviour

## TL;DR

This paper uses movable automata inspired by dragonflies to model animal territorial competition and explores how attraction and repulsion affect behavior.

## Contribution

The study introduces a novel model using movable automata to simulate animal territorial behavior with attraction and repulsion dynamics.

## Key findings

- Faster males exhibit velocity distributions similar to Maxwell distributions in Brownian dynamics.
- Smaller animals are concentrated in regions of small velocities and areas.
- Larger animals spend more time surrounded by smaller ones and are slowed by interactions.

## Abstract

We explore the use of movable automata in numerical modelling of male competition for territory. We used territorial dragonflies as our biological inspiration for the model, assuming two types of competing males: (a) faster and larger males that adopt a face‐off strategy and repulse other males; (b) slower and smaller males that adopt a non‐aggressive strategy. The faster and larger males have higher noise intensity, leading to faster motion and longer conservation of motion direction. The velocity distributions resemble the Maxwell distributions of velocity, expected in Brownian dynamics, with two probable velocities and distribution widths for the two animal subpopulations. The fast animals' trajectories move between visually fixed density folds of the slower animal subpopulation. A correlation is found between individual velocity and individual area distribution, with smaller animals concentrated in a region of small velocities and areas. Attraction between animals results in a modification of the system behaviour, with larger animals spending more time being surrounded by smaller animals and being slowed down by their interaction with the surroundings. Overall, the study provides insights into the dynamics of animal competition for territory and the impact of attraction between animals.

Modelling competition for territory in animals is widespread technique but lack the implementation of multiple variables in editable scenarios. We used movable automata, inspired by territorial dragonflies to provide new insights into the dynamics of animal competition for territory and the impact of attraction/repulsion between animals.