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The synchronization transitions in Newman-Watts small-world neuronal networks (SWNNs) induced by time delayand long-range connection (LRC) probabilityhave been investigated by synchronization parameter and space-time plots. Four distinct parameter regions, that is, asynchronous region, transition region, synchronous region, and oscillatory region have been discovered at certain LRC probabilityas time delay is increased. Interestingly, desynchronization is observed in oscillatory region. More importantly, we consider the spatiotemporal patterns obtained in delayed Newman-Watts SWNNs are the competition results between long-range drivings (LRDs) and neighboring interactions. In addition, for moderate time delay, the synchronization of neuronal network can be enhanced remarkably by increasing LRC probability. Furthermore, lag synchronization has been found between weak synchronization and complete synchronization as LRC probabilityis a little less than 1.0. Finally, the two necessary conditions, moderate time delay and large numbers of LRCs, are exposed explicitly for synchronization in delayed Newman-Watts SWNNs.

Time Delay and Long-Range Connection Induced Synchronization Transitions in Newman-Watts Small-World Neuronal Networks