Exponential stability for a multi-particle system with piecewise interaction function and stochastic disturbance

In this paper, a generalized Motsch-Tadmor model with piecewise interaction function is investigated, which can be viewed as a generalization of the model proposed in [ 9 ]. Our analysis bases on the connectedness of the underlying graph of the system. Some sufficient conditions are presented to guarantee the system to achieve flocking. Besides, we add a stochastic disturbance to the system and consider the flocking in the sense of expectation. As results, some criterions to the flocking solution with exponential convergent rate are established by the standard differential equations analysis.