【摘要】 在神经元电路中，电容型元件的输出电压可被映射为无量纲变量，其放电模式与生物神经元中检测到的膜电位特征相似。为进一步考虑细胞膜形变效应，在神经元电路中引入忆容器，从而提高模型在不同生理与环境条件下模拟神经元行为的能力。将电容器与忆容器通过线性电阻连接，并与包含电感器和非线性电阻的其它支路电路并联。通过将该神经元电路的物理方程等效转换为神经元理论模型，系统讨论了具有双层膜结构和两个电容变量的神经元电活动特征。推导了一个无量纲神经元模型及其对应的能量函数。将神经元电路的场能量函数转化为等效的哈密顿能量函数，并通过赫姆霍兹定理进一步验证。哈密顿能量函数的平均值可作为预测随机共振发生的指标，并通过分析变异系数分布曲线进行验证。结果表明，神经元放电模式与能量水平密切相关。因此，提出一种自适应控制策略来调节神经元电活动的模态转迁。构建了等效模拟电路以验证数值结果，进而证明了该神经元模型的可靠性。更多还原

【Abstract】 The output voltages for the capacitive elements of a neural circuit model can be mapped into dimensionless capacitive variables, which present firing patterns similar to the membrane potentials detected in biological neurons. The inclusion of a memcapacitor also enables consideration of membrane deformation effects, enhancing the model’s capacity to simulate neuronal behavior across varying physiological and environmental conditions. In this study, a capacitor and a memcapacitor are connected through a linear resistor in parallel with other electric components in different branch circuits composed of an inductor and a nonlinear resistor. The electrical activities in a neuron with a double-layer membrane and two capacitive variables are discussed in detail after converting the nonlinear equations for the neural circuit into a theoretical neuron model. A dimensionless neuron model and its corresponding energy function are derived. The field energy function for the neural circuit is converted into an equivalent Hamilton energy function and further validated via the Helmholtz theorem. Furthermore, the average value of energy serves as an indicator for predicting stochastic resonance, as supported by analyzing the distribution of the coefficient of variation. The neuronal firing patterns are shown to be energy-dependent. An adaptive control strategy is proposed to regulate mode transitions in electrical activities of the neuron. An analog equivalent circuit is constructed to experimentally verify the numerical results, thereby supporting the reliability of the proposed neuron model.更多还原