Switch elements with S-shaped current-voltage characteristic in models of neural oscillators

Abstract

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.