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

Abstract

We present a new stochastic particle system on networks which exhibits flocking behavior and pattern formation. More precisely, we consider Cucker–Smale particles with decentralized formation control and multiplicative noises on symmetric 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 does not require any spectral information of the graph associated with the network structure.