2015/10/12 by Florian Gomez, Tom Lorimer, Gomez, Florian +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #nlin.AO #physics.bio-ph #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1510.03241
arxiv created 2015/10/12 · openalex publication_date 2015/10/12 · arxiv updated 2015/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.