# Collective dynamics of opposing groups with stochastic communication

## TL;DR

This paper models the collective behavior of two opposing groups with stochastic communication, demonstrating that over time, groups tend to separate with low internal variation and significant inter-group distance, supported by simulations.

## Contribution

It introduces a new stochastic model for opposing groups, analyzing their long-term separation behavior and providing theoretical and numerical validation.

## Key findings

- Groups tend to separate over time with low internal variation.
- The model predicts persistent separation between opposing groups.
- Numerical simulations confirm theoretical results.

## Abstract

We propose models describing the collective dynamics of two opposing groups of individuals with stochastic communication. Individuals from the same group are assumed to align in a stochastic manner, while individuals from different groups are assumed to anti-align. Under reasonable assumptions, we prove the large time behavior of separation, in the sense that the variation inside a group is much less than the distance between the two groups. The separation phenomena are verified by numerical simulations.