Stochastic flocking dynamics of the Cucker–Smale model with multiplicative white noises

We present a strong asymptotic stochastic flocking estimate for the stochastically perturbed Cucker–Smale model. We characterize a form of multiplicative white noises and present sufficient conditions on the control parameters to guarantee the almost sure exponential convergence toward constant equilibrium states. When the strength of multiplicative noises is sufficiently large, we show that the strong stochastic flocking occurs even for negative communication weights.