Influence of Time Delay and Noise on Critical Coupling Parameter in Synchronization of Small World Neural Networks

The influence of time delay and noise on critical coupling parameter in the synchronization of small world neural networks is investigated. We find that the time delay and noise play important role in synchronization of this extended system. We find that the time delay presents, the quality of the synchronization of neural network worsens. However, the present of noise results more worsens in the quality of the synchronization of network. One can see that the qualitative relation between critical coupling parameter and linked degree: the larger linked degree becomes, the larger critical coupling parameter with time delay and noise absent or present. This trend is influenced by time delay and noise. The trend become steeper when time delay present, and more gently when noise present.