The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.

本文的目的是探索有色噪声的神经系统中的非周期性随机共振现象。对于由高斯有色噪声驱动的非线性动力系统，我们证明了随机样本轨迹可以收敛到相应的确定性轨迹，因为噪声强度分别在全局和局部 Lipschitz 条件下均方趋于零。然后，根据禁区间定理，我们预测了双稳态和可兴奋神经系统中的非周期性随机共振现象。两个神经元模型进一步用于验证理论预测。此外，我们揭示了由相关时间引起的非周期性随机共振现象，这一发现表明调整噪声相关性可能是神经信号处理中生物学上更合理的机制。