Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

Astounding properties of biological sensors can often be mapped onto a dynamical system below the occurrence of 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...

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Bibliographic Details
Published inPhysical review letters Vol. 116; no. 10; p. 108101
Main Authors Gomez, Florian, Lorimer, Tom, Stoop, Ruedi
Format Journal Article
LanguageEnglish
Published United States 11.03.2016
Subjects
Cochlea - innervation
Hair Cells, Vestibular - physiology
Models, Neurological
Nerve Net - physiology
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Summary:Astounding properties of biological sensors can often be mapped onto a dynamical system below the occurrence of 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 dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., neuronal Hodgkin-Huxley equations). When subject to natural "signal coupling," ensembles of Hopf systems below the bifurcation threshold exhibit a collective Hopf bifurcation. This collective Hopf bifurcation occurs at parameter values substantially below where the average of the individual systems would bifurcate, with a frequency profile that is sharpened if compared to the individual systems.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.116.108101