A Qualitative Approach for the Design of a Locally Active Memristor Based Neuron Circuit

Neuromorphic circuit design utilizing emergent memory technologies has been recently popular due to the rich intrinsic dynamics accommodating in nanoscale devices, namely in threshold switches or locally active memristors (LAMs). In this work, we introduce a qualitative approach for the design of a locally active memristor based 2nd order bio-inspired neuron circuit. We initially examine the phase plane characteristics of the 2nd order biologically plausible INa,p+IK neuron model and compare them with the same characteristics of the LAM based Leaky integrate and Fire (LIF) neuron circuit. Consequently, we define the current of the LAM as the spiking variable and voltage of the parallel capacitor as the recovery variable for the LIF circuit. Then, in order to match the phase plane characteristics of the INa,p+IK model, we adopt a qualitative approach and modify the LIF circuit by replacing the linear bias resistor with a nonlinear counterpart with a sinh nonlinearity. This way, we show that the proposed circuit can better capture the neuronal dynamics of the INa,p+IK model and exhibit distinctive features such as the co-existence of resting and limit cycle states. Our future work should cover quantitative analysis for the precise implementation of the neuronal dynamical features.