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Signal-coupled Hopf-type systems show a sharpened collective response


Gomez, F; Lorimer, T; Stoop, R (2016). Signal-coupled Hopf-type systems show a sharpened collective response. Physical Review Letters, 116(10):online.

Abstract

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 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.

Abstract

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 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2016
Deposited On:22 Feb 2016 09:48
Last Modified:30 Oct 2016 08:46
Publisher:American Physical Society
Series Name:Physical Review Letters
ISSN:0031-9007
Publisher DOI:https://doi.org/10.1103/PhysRevLett.116.108101
Official URL:https://journals.aps.org/prl/accepted/05072Y42U3e10e5984cc9687eb246edd06c23c5b9

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