In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times $\tau$ and ${\tau }_0$ can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay $\alpha$ and the correlation time $\tau$ of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time ${\tau }_0$ of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

在本文中，我们重点研究由乘性非高斯有色噪声和加性高斯有色噪声引起的时滞 FitzHugh-Nagumo 系统的随机稳定性和随机共振（SR）现象。利用快速下降法、统一有色噪声近似和SR的二态理论，得到不同噪声项和时延引起的平稳概率密度函数（SPDF）和信噪比（SNR）被探索。研究结果表明，两种噪声强度、时延以及与高斯噪声的偏离参数都会降低两种稳定状态周围的概率密度，破坏神经系统的稳定性；而两个噪声相关时间$\tau$和${\tau }_0$既可以提高两个稳定状态周围的概率密度，又可以增强神经系统的生物稳定性。对于SNR，发现两种噪声强度和偏离系数都会减弱SR效应，而时延会减弱SR效应。$\alpha$和相关时间$\tau$乘性噪声的增加总是会放大 SR 现象。值得一提的是，相关时间${\tau }_0$加性噪声的大小可以刺激 SR 效应，但不会改变 SNR 的最大值。