Angle restriction enhances synchronization of self-propelled objects
Jianxi Gao, Shlomo Havlin, Xiaoming Xu, Harry Eugene Stanley · Physical Review E · 2011
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 ${\ensuremath{\theta}}_{R}$. 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 ${\ensuremath{\theta}}_{R}$, the change is replaced by ${\ensuremath{\theta}}_{R}$. We find that (i) counterintuitively, the synchronization improves significantly when ${\ensuremath{\theta}}_{R}$ decreases, (ii) there exists a critical restricted angle ${\ensuremath{\theta}}_{Rc}$ at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude $\ensuremath{\eta}$, the synchronization as a function of ${\ensuremath{\theta}}_{R}$ shows a maximum value, indicating the existence of an optimal ${\ensuremath{\theta}}_{R}$ that yields the best synchronization for every $\ensuremath{\eta}$.