title: Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response.
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 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.
authors.affiliation: Institute of Neuroinformatics and Institute of Computational Science, University of Zurich and ETH Zurich, 8057 Zurich, Switzerland.
authors.forename: Florian
authors.initials: F
authors.lastname: Gomez
authors.affiliation: Institute of Neuroinformatics and Institute of Computational Science, University of Zurich and ETH Zurich, 8057 Zurich, Switzerland.
authors.forename: Tom
authors.initials: T
authors.lastname: Lorimer
authors.affiliation: Institute of Neuroinformatics and Institute of Computational Science, University of Zurich and ETH Zurich, 8057 Zurich, Switzerland.
authors.forename: Ruedi
authors.initials: R
authors.lastname: Stoop
mesh_terms: D003051:Cochlea / Q000294:innervation*; D018069:Hair Cells, Vestibular / Q000502:physiology*; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology