Flocking and collision avoidance problem of a singular Cucker–Smale model with external perturbations

In order to study the influence of external force or external perturbation on flocking behavior, a Cucker–Smale flocking model with singular communication weight and perturbation functions is proposed. By imposing appropriate restrictions on the perturbation functions, we first prove the system does not allow any collisions between agents under certain initial conditions. Moreover, under the same conditions, we obtain the system has an asymptotic flocking. Last, we give specific examples of perturbation functions and verify the correctness of the results through numerical simulations.