On the Contraction of Excitable Systems

TL;DR

This paper investigates how contraction properties of the Hodgkin-Huxley model affect spike timing reliability, showing contraction depends on input sparsity and firing rate.

Contribution

It demonstrates that the Hodgkin-Huxley model remains contractive under certain conditions, influencing spike timing reliability.

Findings

Model is contractive without input in physiological regions.

Contraction persists with sparse impulsive inputs.

High input firing rates break contraction, reducing reliability.

Abstract

We study the contraction of Hodgkin-Huxley model and its role in the reliability of spike timings. Without input, the model is contractive in the region of physiological interest. With impulsive synaptic inputs, contraction is retained provided that the input events are sparse enough. Contraction is lost when the input firing rate is too high. Spike timings are shown to be reliable in the contracting regime.