The impedance of spiking neurons coupled by time-delayed interaction

The synchronization of populations of interacting spiking neurons is a topic of interest for understanding the operation of the brain and for developing oscillatory-based biomimetic computation. The analysis of the operation of neurons by models such as Hodgkin-Huxley (HH) and FitzHugh-Nagumo (FHN) is based on the electrical and electrochemical concepts. The application of small-signal AC impedance and equivalent circuit methods is a promising tool for the fabrication of artificial neurons and synapses with memristor technologies for neuromorphic computation and sensory-motor autonomous systems. The time domain and impedance spectroscopy analysis of two FHN neurons coupled with a time delay related to the propagation of the action potentials is developed. Depending on the coupling strength and delay time constant, the two neurons become synchronized, in phase opposition for a weak coupling, and in alternating spike packets for the strong interaction. The delayed interaction introduces a new element in the equivalent circuit. A new oscillatory impedance that causes curling of the basic spectral patterns associated with the onset of a limit cycle in the presence of Hopf bifurcations is found. The new pattern is appealing as an experimental tool to determine experimentally the extent of coupling between neurons. (© 2022 The Authors. physica status solidi (a) applications and materials science published by Wiley‐VCH GmbH)