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

Understand

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.