THE MOTSCH-TADMOR MODEL WITH MULTIPLICATIVE WHITE NOISES IN FLOCKS

We enlarge the range of critical exponent β of the communication rate for unconditional flocking in the model proposed by Motsch, S. and Tadmor, E. [J. Statist. Phys., 141 (2011), 923–947], and describe an asymmetric stochastic model which emphasizes the asymmetric interaction between agents and employs the multiplicative white noise for the stochastic forces acting on ith-agent. For the case of asymmetric communication rate, we present sufficient conditions to guarantee the strong stochastic flocking to occur and show the almost sure exponential convergence toward constant equilibrium state through the control of the parameters and initial data. Our results are illustrated through the numerical simulations.