Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks

Abstract Most previous studies assumed noise to be unbounded Gaussian. Here the effects of non-Gaussian cross-correlated sine-Wiener (CCSW) bounded noises on temporal regularity and spatial synchronization of coupled neurons are investigated in regular and small-world networks of the FitzHugh–Nagumo (FHN) neurons. For regular neuronal networks, as cross-correlation time of CCSW noises is increased, CCSW noises-induced temporal coherent resonance occurs at appropriately cross-correlation time of CCSW noises, and spatial synchronization in neuronal network is always impaired. In addition, the increasing degree of correlation of CCSW noises may enhance or impair temporal regularity, which is dependent on cross-correlation time. On the other hand, the increasing degree of correlation of CCSW noises destroys spatial synchronization or has no effect on spatial synchronization. For small world neuronal network, CCSW noises-induced enhancement of temporal regularity and degradation of spatial synchronization are still observed. Furthermore, the increasing rewiring probability make spatiotemporal pattern more order in time and in space. If delay is introduced into small world network, the aforementioned CCSW noises-induced phenomena still exist. Meanwhile, delay let spatiotemporal pattern more disorder.

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