α-stable noise-induced coherence on a spatially extended Fitzhugh–Nagumo system

Abstract

In this paper, we study the noise-induced temporal and spatial coherence in a spatially extended Fitzhugh–Nagumo (FHN) neuronal system. The system is modeled by a randomly connected small-world network, in which an -stable noise is imposed on the first neuron. We focus on the impact of additive temporally and spatially uncorrelated non-Gaussian -stable noise that determines the interactions amongst coupled FHN neurons. Using numerical simulations, we find that the system presents a typical coherence characteristic on temporal scale, while a decoherence characteristic on spatial scale. Then, the temporal and spatial coherence under the influences of -stable noises are studied, respectively. We find that has a significant impact on the temporal coherence but little significance on the spatial coherence. It shows that in contrast to Gaussian noise, -stable noises lead to poor temporal coherence.