Memristor (memory resistor) is a passive electrical circuit element
whose instantaneous resistance depends not only on the voltage, but the
history of the voltage applied to it. The first memristor was
fabricated in 2008 by the HP labs in a semiconductor titanium-dioxide
thin film. It provided the first example where the microscopic
mechanism - the motion of dopant ions - responsible for the memory
resistor is well understood. Apart from its potential for high-density
memory storage, the electrical properties of a memristor share
similarities with those of ion channels in biological membranes
including axons. The electrical response of an axon is traditionally
modeled using Hodgkin-Huxley equations, along with phenomenologically
determined voltage-dependent parameters. However, in contrast to the
memristor case, a microscopic derivation of these parameters is neither
well-understood nor straightforward. Our objective is to determine and
investigate the memristive circuits that can mimic the
action-potential-like response of a neuron. To that end, we will
numerically obtain the current-voltage behavior of Hodgkin-Huxley
neuron under steady-state and periodic stimulus current and its
dependence on the phenomenological parameters, and compare the results
with those obtained from the current-voltage characteristics of a
network with a number of memristors. This research may, thus, lead to
the identification of a minimal circuit with inorganic memristors that
displays signatures of a neuron.