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 theta(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 theta(R), the change is replaced by theta(R). We find that (i) counterintuitively, the synchronization improves significantly when theta(R) decreases, (ii) there exists a critical restricted angle theta(Rc) at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude eta, the synchronization as a function of theta(R) shows a maximum value, indicating the existence of an optimal theta(R) that yields the best synchronization for every eta.