Angle restriction enhances synchronization of self-propelled objects

Understanding the synchronization process of self-propelled objects is of great interest in science and technology. We propose a synchronization model for a self-propelled objects system in which we restrict the maximal angle change of each object to θ_R. At each time step, each object moves and changes its direction according to the average direction of all of its neighbors (including itself). If the angle change is greater than a cutoff angle θ_R, the change is replaced by θ_R. We find that (i) counterintuitively, the synchronization improves significantly when θ_R decreases, (ii) there exists a critical restricted angle θ_Rc at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude η, the synchronization as a function of θ_R shows a maximum value, indicating the existence of an optimal θ_R that yields the best synchronization for every η.