逆随机共振分析：神经兴奋性与时标分离的影响
Analysis of inverse stochastic resonance: Effects of neural excitability and timescale separation
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中文总结 AI 辅助
该研究分析双稳FitzHugh–Nagumo神经元的逆随机共振，通过分岔分析、蒙特卡罗模拟等揭示其参数依赖机制，建立逃逸平衡机制关联神经元参数与噪声诱导的尖峰抑制。
中文摘要 AI 辅助
我们分析了由电压变量中的加性噪声驱动的双稳FitzHugh–Nagumo神经元中的逆随机共振（ISR），重点关注神经兴奋性和时标分离如何调节噪声诱导的放电活动调制。余维二分岔分析确定了一个狭窄的双稳区域，其中稳定不动点与稳定极限环共存，二者被不稳定周期轨道分隔。有限时间蒙特卡罗模拟表明，当未完全解析稀有跃迁时，极限环 basin 的占据情况似乎依赖于初始 basin。我们证明这种依赖并非渐近的：只要随机系统具有唯一的不变概率测度，长期放电统计就与初始吸引 basin 无关。ISR 的参数依赖性通过针对退化噪声的几何最小作用方法计算的拟势垒来表征。极限环与不动点的拟势之差将双稳楔分为两个逃逸主导区域。简化的亚稳态两态马尔可夫近似给出了极限环 basin 占据概率的弱噪声公式、真正ISR的符号判据以及ISR最小噪声幅度的半定量预测。在具有负有效指数的拟合区域中，仅当极限环拟势超过不动点拟势时，才会出现真正的ISR最小值。这些结果提供了一种逃逸平衡机制，将内在神经元参数与渐近噪声诱导的尖峰抑制联系起来。
英文摘要
We analyze inverse stochastic resonance (ISR) in a bistable FitzHugh--Nagumo neuron driven by additive noise in the voltage variable, focusing on how neural excitability and timescale separation regulate the noise-induced modulation of spiking activity. A codimension-two bifurcation analysis identifies a narrow bistable region in which a stable fixed point and a stable limit cycle coexist, separated by an unstable periodic orbit. Finite-time Monte Carlo simulations show that the occupation of the limit-cycle basin may appear to depend on the initial basin when rare transitions are not fully resolved. We prove that this dependence is not asymptotic: the stochastic system admits a unique invariant probability measure, so long-time firing statistics are independent of the initial basin of attraction. The parameter dependence of ISR is characterized by quasi-potential barriers computed with a geometric minimum action method for the degenerate noise. The difference between the limit-cycle and fixed-point quasi-potentials partitions the bistable wedge into two escape-dominated regimes. A reduced metastable two-state Markov approximation yields a weak-noise formula for the limit-cycle basin occupation probability, a sign criterion for genuine ISR, and a semiquantitative prediction of the ISR-minimizing noise amplitude. In the fitted regime with a negative effective exponent, a genuine ISR minimum occurs only when the limit-cycle quasi-potential exceeds that of the fixed point. These results provide an escape-balance mechanism linking intrinsic neuronal parameters to asymptotic noise-induced spike suppression.
