论文标题
关于具有恒定信号的单随机霍奇金神经元的长时间行为，以及相互作用的神经元电路的构造，显示自组织的节奏振荡
On the long time behaviour of single stochastic Hodgkin-Huxley neurons with constant signal, and a construction of circuits of interacting neurons showing self-organized rhythmic oscillations
论文作者
论文摘要
本文中考虑的随机霍奇金 - 赫克斯利神经元取代了随机过程的$ \ vartheta dt + dx_t $替换了经典确定性模型的时间范围的确定性输入$ 信号。对于该过程的各种功能，我们具有大量的千古和强大定律，并将“安静的行为”和“常规峰值”表征为概率取决于参数$（τ，σ）$以及信号$ \ vartheta $的事件。安静的行为和常规峰值的概念可以构建相互作用的随机霍奇金 - 赫克斯利神经元的电路，将激发与沿电路的集体结构结合在一起，可以观察到自组织的节奏振荡。
The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with volatility $σ>0$ and backdriving force $τ>0$, and we call $\vartheta>0$ the signal. We have ergodicity and strong laws of large numbers for various functionals of the process, and characterize 'quiet behaviour' and 'regular spiking' as events whose probability depends on the parameters $(τ,σ)$ and on the signal $\vartheta$. The notions of quiet behaviour and regular spiking allow for a construction of circuits of interacting stochastic Hodgkin-Huxley neurons, combining excitation with inhibition according to a bloc structure along the circuit, on which self-organized rhythmic oscillations can be observed.
