We find that the fractional-order Hindmarsh-Rose model neuron demonstrates various types of firing behavior as a function of the fractional order in this study.There exists a clear difference in the bifurcation diagram between the fractional-order Hindmarsh-Rose model and the corresponding integer-order model even though the neuron undergoes a Hopf bifurcation to oscillation and then starts a period-doubling cascade to chaos with the decrease of the externally applied current.Interestingly,the discharge frequency of the fractional-order Hindmarsh-Rose model neuron is greater than that of the integer-order counterpart irrespective of whether the neuron exhibits periodic or chaotic firing.Then we demonstrate that the firing behavior of the fractional-order Hindmarsh-Rose model neuron has a higher complexity than that of the integer-order counterpart.Also,the synchronization phenomenon is investigated in the network of two electrically coupled fractional-order model neurons.We show that the synchronization rate increases as the fractional order decreases.
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.
