  In this paper, we present circuit solutions based on a switch element with
the S-type I-V characteristic implemented using the classic FitzHugh-Nagumo and
FitzHugh-Rinzel models. Using the proposed simplified electrical circuits
allows the modeling of the integrate-and-fire neuron and burst oscillation
modes with the emulation of the mammalian cold receptor patterns. The circuits
were studied using the experimental I-V characteristic of an NbO2 switch with a
stable section of negative differential resistance (NDR) and a VO2 switch with
an unstable NDR, considering the temperature dependences of the threshold
characteristics. The results are relevant for modern neuroelectronics and have
practical significance for the introduction of the neurodynamic models in
circuit design and the brain-machine interface. The proposed systems of
differential equations with the piecewise linear approximation of the S-type
I-V characteristic may be of scientific interest for further analytical and
numerical research and development of neural networks with artificial
intelligence.
