Impact of bounded noise and shortcuts on the spatiotemporal dynamics of neuronal networks

The influences of bounded noise together with shortcuts on the spatiotemporal collective behaviors of temporal coherence and spatial synchronization are discussed in neuronal networks. Firstly, we focus on the case of regular neuronal networks. With the increase of noise amplitude, we find that the spatial synchronizability among coupled neurons is always impaired and coherence resonance, however, occurs at an appropriately tuned level of noise amplitude. Then, we introduce shortcuts to the regular neuronal networks to formulate small-world neuronal networks. The results indicate that the spatial synchronization and temporal coherence in the networks can be enhanced with the addition of shortcuts. Moreover, we verify that there exists an optimal amount of added shortcuts such that the small-world networks reach much more ordered spatiotemporal patterns, i.e., coupled neurons are nearly synchronized in space and most coherent in time. In addition, the shortcuts-induced much more ordered states are confirmed to be robust against changes of the intensity of the unit Wiener process.