A memristor-based circuit approximation of the Hindmarsh-Rose model

Neuron models exist in different levels of complexity and biological modeling depth. The Hindmarsh-Rose model offers a rich repertoire of neuronal dynamics while being moderately mathematically complex. Existing circuit realizations of this neuron model, however, require a large amount of operational amplifiers due to the model's quadratic and cubic nonlinearity. In contrast to hardware realizations of simpler neuron models, this leads to a higher power consumption. In this work, the Hindmarsh-Rose model is approximated by an ideal electrical circuit that relies mostly on passive circuit elements and thus reduces the power consumption. For this purpose, we analyze the power flows of an equivalent electrical circuit of the Hindmarsh-Rose model and replace several nonlinear circuit elements by constant ones. Moreover, we approximate the cubic nonlinearity by three memristors in combination with a negative impedance converter. This negative impedance converter represents the only active circuit element required for the complete circuit, leading to an increased energy efficiency compared to the existing circuit realizations. Simulations verify the circuit's ability to generate spiking and bursting dynamics comparable to the original Hindmarsh-Rose model.