Controlled pattern formation of stochastic Cucker-Smale systems with network structures

TL;DR

This paper introduces a stochastic particle system on networks modeling flocking and pattern formation, proving asymptotic behavior without spectral graph assumptions.

Contribution

It develops a new stochastic Cucker-Smale model with decentralized control and multiplicative noise on networks, analyzing flocking and pattern formation.

Findings

Proves time-asymptotic stochastic flocking behavior.

Establishes pattern formation under network structures.

Uses Lyapunov functional estimates without spectral graph info.

Abstract

We present a new stochastic particle system on networks which describes the flocking behavior and pattern formation. More precisely, we consider Cucker-Smale particles with decentralized formation control and multiplicative noises on symmetric and connected networks. Under suitable assumptions on the initial configurations and the network structure, we establish time-asymptotic stochastic flocking behavior and pattern formation of solutions for the proposed stochastic particle system. Our approach is based on the Lyapunov functional energy estimates, and it does not require any spectral information of the graph associated with the network structure.