Hopf-type neurons increase input-sensitivity by forming forcing-coupled ensembles
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.
Cite
@article{arxiv.1510.03241,
title = {Hopf-type neurons increase input-sensitivity by forming forcing-coupled ensembles},
author = {Florian Gomez and Tom Lorimer and Ruedi Stoop},
journal= {arXiv preprint arXiv:1510.03241},
year = {2015}
}