Complete synchronization in the globally delay-coupled Hindmarsh-Rose large-scale network

Synchronization is a common phenomenon in coupled systems of the world, especially in complex networks combined with nonlinear oscillators. In real world, a problem of signal transfer which is unavoidable is delays in the system. In this paper, we studied the complete synchronization of the globally delay-coupled Hindmarsh-Rose network with a large scale. During the simulations and calculations, we found that although the delay in the gap junction may desynchronize two coupled Hindmarsh-Rose oscillators, it can reduce the demand of synchronization in a large scale network. Through the simulation results, we guess the elimination of chaos in the network might be the reason why the delay can enhance the ability of synchronization in large-scale networks. We defined a quantitative indicator called period error to prove our presumption, and indicate that the proper period of delay which can synchronize a large scale network don´t have many relationship with the scale of the network when the coupling strength is in inverse proportion to the scale of the network.