Stochastic noise exists widely in the nervous system, and noise plays an extremely important role in the information processing of the nervous system. Noise can enhance the ability of neurons to process information as well as decrease it. For the dynamic behavior of stochastic resonance and coherent resonance shown by neurons under the action of stochastic noise, this paper uses Fourier coefficient and coherence resonance coefficient to measure the behavior of stochastic resonance and coherence resonance, respectively, and some conclusions are drawn by analyzing the effects of additive noise and multiplicative noise. Appropriate noise can make the nonlinear system exhibit stochastic resonance behavior and enhance the detection ability of external signals. It can also make the coherent resonance behavior of the nonlinear system reach its optimal state, and the system becomes more orderly. By comparing the effects of additive and multiplicative noise on the stochastic resonance behavior and coherent resonance behavior of the system, it is found that additive and multiplicative noise can both make the system appear the phenomenon of stochastic resonance and have almost identical discharge state at the same noise intensity. However, with the increase of noise intensity, the coherent resonance of the system occurs, the multiplicative noise intensity is smaller than that of additive noise, but the coherent resonance coefficient of additive noise is smaller and the coherent resonance effect is better. The system whose system parameters are located near the bifurcation point is more prone to coherent resonance, and the closer the bifurcation point is, the more obvious the coherent resonance phenomenon is, and the more regular the system becomes. When the parameters of the system are far away from the bifurcation point, the coherent resonance will hardly appear. Besides, when additive and multiplicative noise interact together, the stochastic resonance and coherent resonance phenomena are more likely to appear at small noise, and the behavior of stochastic resonance and coherent resonance that the system shown is better in the local range.

中文翻译：

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白噪声刺激下 FitzHugh-Nagumo 神经元的随机动态行为

随机噪声广泛存在于神经系统中，噪声在神经系统的信息处理中起着极其重要的作用。噪声可以增强神经元处理信息的能力，也可以降低它。针对神经元在随机噪声作用下表现出的随机共振和相干共振的动态行为，本文分别使用傅里叶系数和相干共振系数来衡量随机共振和相干共振的行为，并通过分析加性噪声和乘性噪声的影响。适当的噪声可以使非线性系统表现出随机共振行为，增强对外部信号的检测能力。它还可以使非线性系统的相干共振行为达到最佳状态，系统变得更加有序。通过比较加性和乘性噪声对系统随机共振行为和相干共振行为的影响，发现加性和乘性噪声都可以使系统出现随机共振现象，同时具有几乎相同的放电状态噪声强度。但随着噪声强度的增加，系统会发生相干共振，乘性噪声强度小于加性噪声，但加性噪声的相干共振系数更小，相干共振效果更好。系统参数位于分岔点附近的系统更容易发生相干共振，分岔点越近，相干共振现象越明显，系统越规则。当系统参数远离分岔点时，几乎不会出现相干共振。此外，当加性和乘性噪声相互作用时，随机共振和相干共振现象更容易出现在小噪声下，系统表现出的随机共振和相干共振行为在局部范围内更好。当系统参数远离分岔点时，几乎不会出现相干共振。此外，当加性和乘性噪声相互作用时，随机共振和相干共振现象更容易出现在小噪声下，系统表现出的随机共振和相干共振行为在局部范围内更好。当系统参数远离分岔点时，几乎不会出现相干共振。此外，当加性和乘性噪声相互作用时，随机共振和相干共振现象更容易出现在小噪声下，系统表现出的随机共振和相干共振行为在局部范围内更好。