双色噪声激励下FHN神经元系统的稳态性质

摘要

Making use of the unified colored noise approximation, the steady sate characteristics of the one-dimensional FitzHugh-Nagumo neural system with two different kinds of colored noises are investigated. The expressions of the steady state probability distribution function and the mean value are obtained. After numerical calculation, the results show that the self-correlated time of the multiplicative noise T1, the self-correlated time of the additive noise T2,the intensity of the additive noise a, and the intensity of the multiplicative noise D can induce the transition. The increases of a and D are conducive to the switch from the exciting state to the resting state. However, with Tl and Tz increasing, the switch from the resting state to the exciting state becomes obvious. The noise intensity and corresponding self-correlated time play opposite roles.%应用统一色噪声理论研究了双色噪声激励下一维FitzHugh—Nagumo（FHN）神经元系统的动力学性质，即稳态概率分布函数和其平均值．给出了FHN神经元系统的稳态概率密度和平均值的解析表达式．结果表明：乘性噪声的自关联时间T1、加性噪声的自关联时间T2、加性噪声强度＆和乘性噪声强度D都能够诱导非平衡相变的产生．at和D的增大有利于系统从激发态向静息态转换．T1，T2的增大有利于系统从静息态向激发态转换．噪声强度和其自关联时间的作用完全相反．