IEEE Trans Biomed Circuits Syst. 2010 Oct;4(5):320-8. doi: 10.1109/TBCAS.2010.2051224.
In this paper, the nonlinear dynamical phenomenon associated with a silicon neuron are described. The neuron has one transient sodium (activating and inactivating) channel and one activating potassium channel. These channels do not model specific equations; instead they directly mimic the desired voltage clamp responses. This allows us to create silicon structures that are very compact (six transistors and three capacitors) with activation and inactivation parameters being tuned by floating-gate (FG) transistors. Analysis of the bifurcation conditions allow us to identify regimes in the parameter space that are desirable for biasing the circuit. We show a subcritical Hopf-bifurcation which is characteristic of class 2 excitability in Hodgkin-Huxley (H-H) neurons. We also show a Hopf bifurcation at higher values of stimulating current, a phenomenon also observed in real neurons and termed excitation block. The phenomenon of post-inhibitory rebound and frequency preference are displayed and intuitive explanations based on the circuit are provided. The compactness and low-power nature of the circuit shall allow us to integrate a large number of these neurons on a chip to study complicated network behavior.
本文描述了与硅神经元相关的非线性动力学现象。该神经元具有一个瞬时钠（激活和失活）通道和一个激活钾通道。这些通道不模拟特定的方程；相反，它们直接模拟所需的电压箝位响应。这使得我们能够创建非常紧凑的硅结构（六个晶体管和三个电容器），激活和失活参数由浮栅（FG）晶体管调节。分岔条件的分析使我们能够确定参数空间中的区域，这些区域有利于为电路偏置。我们展示了一个亚临界 Hopf 分岔，这是 Hodgkin-Huxley（H-H）神经元中 2 类兴奋性的特征。我们还展示了在更高刺激电流值处的 Hopf 分岔，这也是在真实神经元中观察到的现象，称为兴奋阻断。后抑制反弹和频率偏好的现象被显示出来，并基于电路提供了直观的解释。该电路的紧凑性和低功耗特性将使我们能够在一个芯片上集成大量的这些神经元，以研究复杂的网络行为。
