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.

Automated summary

This paper investigates the synchronization of neurons and its significance in understanding brain function and developing neural computation. By analyzing FHN neurons, the study discovers new elements and oscillatory impedance introduced by delayed interaction, which has potential applications in determining the extent of coupling between neurons experimentally.