Research on flocking behavior of multi-perturbation Cucker-Smale model

The Cucker-Smale model is a classic model used in the research of multi-agents flocking behavior. In practical applications, the multi-agents system is often affected by multi-perturbation. Considering the above situation, a multi-perturbation Cucker-Smale model is proposed. By constructing and analyzing the Lyapunov function of the model, the initial conditions and the constraints of the position and velocity perturbations in the multi-perturbation Cucker-Smale model are obtained, which enable multi-agents to form asymptotic flocking and collision avoidance. Finally, two numerical examples of the same and different position and velocity perturbations were studied. The results indicate that multi-agents in the multi-perturbation Cucker-Smale model can form asymptotic flocking and collision avoidance under identical position and velocity perturbations. Different position and velocity perturbations will affect the time when the velocity tends to be consistent in multi-agents flocking. However, the multi-agents can still form asymptotic flocking and collision avoidance when the constraints of position and velocity perturbations are satisfied. This further validates the effectiveness of the obtained conclusions.