A rewiring mechanism to improve synchronization in Kuramoto networks

Abstract

Abstract The emergence of synchronization among a set of individual oscillators that are coupled in a network is an amazing physical phenomenon that appears in many different systems, from natural sciences to even human behavior. The phenomenon has attracted the attention of many researchers in many fields of science and engineering by the science behind its unique collective behavior without some kind of external organization. One of the most popular models for the dynamical evolution of coupled phase oscillators is the Kuramoto model, which gives a simple yet powerful formalization together with a numerical measure called the degree of synchronization. The crucial role of structural properties of the network on the degree of synchronization is analyzed in many researches. One of streamlines, well-known as ‘rewiring’, is to re-design the network structure via rearranging its links to increase or decrease the degree of synchronization. In this study, we propose a rewiring mechanism to improve the degree of synchronization for the coupled heterogeneous oscillators based on global and local information of networks. In our mechanism, the share of each link in the maximum eigenvalue of the Laplacian matrix of the network is considered as local information, together with a global criteria which is defined based on frequencies and eigenvectors of the Laplacian matrix. Experimental results show that the proposed mechanism can improve the order parameter in a more stable manner.