Noise Under The Influence Of Group Movement Synchronization Problems

This paper mainly discusses the consensus problem of multiple agents system with noise perturbation which is an omnipresent phenomenon in nature, e.g, the moving of the migrant, the dispersal of the crowd and the control of the traffic. The advantages of consensus have been shown in most of such relative fields thus it has emerged as a hot topic recently. The virtual leader framework is a representative model among the collective-motion models because it includes both the internal ef-fects and the external controls. We import the noise term into the above-mentioned framework so as to have a more accurate model. Using the stochastic dynamical systems'theory, we show that the system can approach the synchronization in the sense of probability one under some specific conditions on noise strength. Addition-ally, we consider the conditions where either the leader term or the communication network is relaxed to some extent. We demonstrate numerically that the results may be diversified depending on the types of noise and other restrictions.