In this paper, we show some dynamical and biological mechanisms of the short-term memory (the fixed point attractor) through the toggle switch in the FitzHugh-Nagumo model (FN). Firstly, we obtain the bistable conditions, show the effect of Gaussian noise on the toggle switch, and explain the short-term memory’s switch mechanism by mean first passage time (MFPT). Then, we obtain a Fokker-Planck equation and illustrate the meaning of the monostable and bistable state in the short-term memory. Furthermore, we study the toggle switch under the interaction of network and noise. Meanwhile, we show that network structure and noise play a vital role in the toggle switch based on network mean first passage time (NMFPT). And we illustrate that the modest clustering coefficient and noise are necessary to maintain memories. Finally, the numerical simulation shows that the analytical results agree with it.

中文翻译：

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网络组织的 FitzHugh-Nagumo 模型中由高斯噪声引起的自发活动

在本文中，我们通过 FitzHugh-Nagumo 模型（FN）中的拨动开关展示了短期记忆（定点吸引子）的一些动力学和生物学机制。首先，我们获得了双稳态条件，展示了高斯噪声对拨动开关的影响，并通过平均首次通过时间（MFPT）解释了短期记忆的开关机制。然后，我们得到了一个 Fokker-Planck 方程，并说明了短时记忆中单稳态和双稳态的含义。此外，我们研究了网络和噪声相互作用下的拨动开关。同时，我们表明网络结构和噪声在基于网络平均首次通过时间（NMFPT）的拨动开关中起着至关重要的作用。我们说明适度的聚类系数和噪声是维持记忆所必需的。最后，