  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.
