弱噪声诱导的跃迁与神经振荡的抑制和调制
Weak-noise-induced transitions with inhibition and modulation of neural oscillations
摘要：
我们分析了弱噪声引起的跃迁对FitzHugh-Nagumo神经元模型动力学行为的影响，该模型处于一个由稳定的不动点和稳定的非受迫极限环组成的稳定状态.分岔和快慢分析给出了建立这种双稳定性的参数空间条件。在双稳态参数区，弱噪声幅值可以强烈抑制神经元的发放活动。令人惊讶的是，增加噪声强度导致尖峰活动的最小值，之后活动开始随着噪声强度的增加而单调增加。我们调查这种抑制和调制的神经振荡弱噪声振幅的变化，每单位时间内的尖峰的平均数与噪声强度。当初始条件位于稳定极限环的吸引区域内时，这种现象总是发生。对于稳定不动点的吸引区域中的初始条件，然而，这种现象消失，除非模型的时间尺度分离参数有界于某个区间内。我们提供了一个理论解释这种现象的随机灵敏度函数的吸引子和他们的最小马哈拉诺比斯距离的分界线隔离的吸引盆地。
英文摘要：
We analyze the effect of weak-noise-induced transitions on the dynamics of the FitzHugh-Nagumo neuron model in a bistable state consisting of a stable fixed point and a stable unforced limit cycle. Bifurcation and slow-fast analysis give conditions on the parameter space for the establishment of this bi-stability. In the parametric zone of bi-stability, weak-noise amplitudes may strongly inhibit the neuron's spiking activity. Surprisingly, increasing the noise strength leads to a minimum in the spiking activity, after which the activity starts to increase monotonically with increase in noise strength. We investigate this inhibition and modulation of neural oscillations by weak-noise amplitudes by looking at the variation of the mean number of spikes per unit time with the noise intensity. We show that this phenomenon always occurs when the initial conditions lie in the basin of attraction of the stable limit cycle. For initial conditions in the basin of attraction of the stable fixed point, the phenomenon however disappears, unless the time-scale separation parameter of the model is bounded within some interval. We provide a theoretical explanation of this phenomenon in terms of the stochastic sensitivity functions of the attractors and their minimum Mahalanobis distances from the separatrix isolating the basins of attraction.
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