Dynamic property analysis and circuit implementation of simplified memristive Hodgkin–Huxley neuron model

In this paper, the dynamic properties of a simplified memristive Hodgkin–Huxley (SMHH) neuron model are analyzed and an electric circuit is designed to completely implement it based on the mathematical equation. The sodium ion channel and potassium ion channel in the SMHH neuron model can be regarded as a second-order memristor and a first-order memristor, respectively. Under different stimuli, the SMHH neuron model can present spiking or bursting activities. In particular, when a periodic sinusoidal current is imposed on the neuron, the electrical activity behaves as bursting and it has a close frequency dependence on the external forcing current. The initiation current value of bursting activity first increases and then drops with the increase in stimulus frequency of the periodic sinusoidal current, which shows an inconsistency in traditional neural adaptation. The potential mechanism is that the frequency-dependent property of the ion channel memristors affects the threshold dynamics of the SMHH neuron. Furthermore, an analog circuit is designed to completely implement the SMHH neuron model. Since the conductance-based neuron models are mathematical complexity, only few analog circuits are designed for this kind of neuron models, which indicates that the designed circuit unit in this work will provide a great convenience to study the dynamics of conductance-based neuron and even collective behaviors of neural networks at circuit level.