Abstract
The synchronization transitions in Newman-Watts small-world neuronal networks (SWNNs) induced by time delay and long-range connection (LRC) probability have 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 probability as 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 probability is 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.
Highlights
Synchronization phenomena are common in nature and can be extensive observed in various realistic systems, especially in neuronal networks, biological systems and ecological systems [1,2]
In this paper we extend the subject by systematically investigating time delay and long-range connection induced synchronization transitions in Newman-Watts small-world neuronal networks (SWNNs)
Lag synchronization has been found between weak synchronization and complete synchronization as long-range connection (LRC) probability P is a little less than 1.0
Summary
Synchronization phenomena are common in nature and can be extensive observed in various realistic systems, especially in neuronal networks, biological systems and ecological systems [1,2]. Synchronization has been widely studied both theoretically and experimentally for decades. Complete synchronization indicates the coincidence of states of coupling systems, X1(t)~X2(t) [3]. Experimental studies have shown that synchronous oscillations can emerge in many special areas of brain, especially in olfactory system or hippocampal region [8,9,10]. Synchronization in neuronal networks and brain systems has attracted much attention. Synchronous oscillations in these systems are related to some specific and important physiological functions, such as olfaction [11], visual perception [12], cognitive processes [13], and information processing [14]
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