Flocking of multi-agent systems with multiplicative and independent measurement noises

• We investigate the Cucker–Smale type system with independent and multiplicative measurement noise.
• The flocking behavior depends on the intensity of noise and the group density.
• We report that, in noise environments, it is rather easy for the group with high density to form and maintain ordered group motion.
• We find that, under the perturbation of multiplicative noise, system with weak coupling can tolerate relatively strong perturbation of noise.

We investigate the effect of noise and group density on the emergence of flocking in a stochastic Cucker–Smale type system. We consider the independent and multiplicative measurement noise and derive sufficient conditions for flocking and non-flocking in terms of the noise intensity and group density. We report that, in noise environments, it is rather easy for the group with high density to form and maintain ordered group motion. Moreover, we find that, under the perturbation of multiplicative noise, systems with weak coupling can tolerate relatively strong perturbation of noise.