# Emergence in Random Noisy Environments

## TL;DR

This paper studies how different dynamical systems exhibit emergent behavior when subjected to random environmental noise, providing conditions for emergence and building on flocking models by Cucker and Smale.

## Contribution

It introduces new sufficient conditions for emergence in dynamical systems under stochastic perturbations, inspired by foundational flocking models.

## Key findings

- Conditions for nearly-emergence identified
- Analysis applicable to multiple dynamical systems
- Builds on and extends flocking model theories

## Abstract

We investigate the emergent behavior of four types of generic dynamical systems under random environmental perturbations. Sufficient conditions for nearly-emergence in various scenarios are presented. Recent fundamental works of F. Cucker and S. Smale on the construction and analysis of flocking models directly inspired our present work.