The phenomenon of stochastic synchronization in globally coupled FitzHugh–Nagumo（FHN） neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation（DMA） and direct simulation（DS）. Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.
With coupled weakly-damped periodically driven bistable oscillators subjected to additive and multiplicative noises under concern, the objective of this paper is to check to what extent the resonant point predicted by the Gaussian distribution assumption can approximate the simulated one. The investigation based on the dynamical mean-field approx- imation and the direct simulation demonstrates that the pre- dicted resonant point and the simulated one are basically co- incident for the case of pure additive noise, but for the case including multiplicative noise the situation becomes some- what complex. Specifically speaking, when stochastic res- onance （SR） is observed by changing the additive noise in- tensity, the predicted resonant point is lower than the sim- ulated one; nevertheless, when SR is observed by chang- ing the multiplicative noise intensity, the predicted resonant point is higher than the simulated one. Our observations im- ply that the Gaussian distribution assumption can not exactly describe the actual situation, but it is useful to some extent in predicting the low-frequency stochastic resonance of the coupled weakly-damped bistable oscillator.
