Synchronization of Kuramoto oscillators in small-world networks

We study the synchronization of Kuramoto oscillators on small-world networks. Firstly, we analyze the impact of coupling strength, rewiring probability and average degree of networks on the phase synchronization in weak coupled system. Then, by increasing the coupling strength, we find an interesting phenomenon that when coupling strength is much larger than the synchronization threshold, there is another threshold which can decrease the synchronization performance of the system. Finally, in order to enhance the synchronization performance of strong coupled system, we adopt a simple way to delete some nodes randomly to construct disordered environment, numerical results show that a certain degree of disorder can promote the synchronization performance of strong coupled small-world networks.