Hopf-type neurons increase input-sensitivity by forming forcing-coupled ensembles

TL;DR

This paper demonstrates that ensembles of Hopf oscillators, coupled through force interactions, can collectively undergo a Hopf bifurcation at lower thresholds, enhancing sensitivity and frequency sharpening in neuronal systems.

Contribution

It introduces the concept of force-coupled Hopf oscillator ensembles exhibiting a collective bifurcation below individual thresholds, explaining biological sensor scale-invariance.

Findings

Ensembles of Hopf oscillators show a collective bifurcation below individual thresholds.

Force-coupling sharpens the frequency profile of the ensemble.

The phenomenon applies broadly to neuronal dynamics near bifurcation points.

Abstract

Astounding properties of biological sensors can often be mapped onto a dynamical system in the vicinity a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from individual hair bundles to whole regions of the cochlea. We reveal here the origin of this scale-invariance, from a general level, applicable to all neuronal dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., Hodgkin-Huxley equations). When coupled by natural 'force-coupling', ensembles of Hopf oscillators below bifurcation threshold exhibit a collective Hopf bifurcation. This collective Hopf bifurcation occurs substantially below where the average of the individual oscillators would bifurcate, with a frequency profile that is sharpened if compared to the individual oscillators.