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

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 multiplicative noises symmetric connected networks. Under suitable assumptions initial configurations network structure, establish time-asymptotic of solutions for proposed system. Our approach is based Lyapunov functional energy estimates, it does not require any spectral information graph associated structure.