Control of stochastic spike motion in an excitable system via recycled noise

Abstract

The control effect of recycled noise, generated by the superposition of a primary Gaussian noise source and a secondary source with a constant delay, has been studied in an excitable FitzHugh-Nagumo system. We mainly focus on the performance of noise-induced spike and coherence resonance in a parameter region sub-threshold to supercritical Hopf bifurcation. For fixed noise intensity, simulations show that the coherence (quantitatively measured by R, which is defined as the mean value of the spike interval time T normalized to its mean square root) and the emission velocity of the noise-induced spikes exhibit damped oscillations with the variation of delay time, demonstrating a new kind of multi-resonance phenomenon. Furthermore, the optimal delay times for resonance and the fast emission velocity are related to the inherent frequency of the system. It seems that there are some synchronization effects between the dynamic character of the system and the delay time of recycled noise. Our results give clear information about how one can control the coherence and emission velocity of the noise-induced spike in a rather effective way, by deliberately adjusting the delay time and the fraction of the secondary noise.