Abstract
Acoustical signal transduction in the cochlea is an active process that involves nonlinear amplification and spontaneous otoacoustic emissions. Signal transduction involves individual subunits composed of globally coupled hair cells, which can be modeled as oscillators close to a Hopf bifurcation. The coupling may induce a transition toward synchronization, which in turn leads to a strong nonlinear response. In the model studied here, the synchronization transition of the subunit is discontinuous (explosive) in the absence of an external stimulus. We show that, in the presence of an external stimulus and for a coupling strength slightly lower than the critical value leading to explosive synchronization, the response of the subunit has better frequency selectivity and a larger signal-to-noise ratio. From physiological observations that subunits are themselves coupled together, we further propose a model of the complete cochlea, accounting for the ensemble of frequencies that the organ is able to detect.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Robles and M. A. Ruggero, Mechanics of the mammalian cochlea, Physiol. Rev. 81, 1305 (2001)
A. Hudspeth, Hearing, in: Principles of Neural Science, 4th Ed., McGraw-Hill, 2000
J. O. Pickles, An Introduction to the Physiology of Hearing, 2nd Ed., Academic Press, 1988
S. S. Narayan, A. N. Temchin, A. Recio, and M. A. Ruggero, Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae, Science 282(5395), 1882 (1998)
J. F. Ashmore, G. S. Géléoc, and L. Harbott, Molecular mechanisms of sound amplification in the mammalian cochlea, Proc. Natl. Acad. Sci. USA 97(22), 11759 (2000)
K. E. Nilsen and I. J. Russell, The spatial and temporal representation of a tone on the guinea pig basilar membrane, Proc. Natl. Acad. Sci. USA 97(22), 11751 (2000)
D. T. Kemp, Stimulated acoustic emissions from within the human auditory system, J. Acoust. Soc. Am. 64(5), 1386 (1978)
R. Probst, B. L. Lonsbury-Martin, G. K. Martin, B. L. Lonsburymartin, and G. K. Martin, A review of otoacoustic emissions, J. Acoust. Soc. Am. 89(5), 2027 (1991)
V. M. Eguíluz, M. Ospeck, Y. Choe, A. J. Hudspeth, and M. O. Magnasco, Essential nonlinearities in hearing, Phys. Rev. Lett. 84(22), 5232 (2000)
S. Camalet, T. Duke, F. Jüicher, and J. Prost, Auditory sensitivity provided by self-tuned critical oscillations of hair cells, Proc. Natl. Acad. Sci. USA 97(7), 3183 (2000)
J. Cartwright, D. González, and O. Piro, Nonlinear dynamics of the perceived pitch of complex sounds, Phys. Rev. Lett. 82(26), 5389 (1999)
K. A. Montgomery, M. Silber, and S. A. Solla, Amplification in the auditory periphery: The effect of coupling tuning mechanisms, Phys. Rev. E 75(5), 051924 (2007)
M. O. Magnasco, A wave traveling over a Hopf instability shapes the cochlear tuning curve, Phys. Rev. Lett. 90(5), 058101 (2003)
T. Duke and F. Jülicher, Active traveling wave in the cochlea, Phys. Rev. Lett. 90(15), 158101 (2003)
P. L. Boyland, Bifurcations of circle maps: Arnol’d tongues, bistability and rotation intervals, Commun. Math. Phys. 106(3), 353 (1986)
A. Kern and R. Stoop, Essential role of couplings between hearing nonlinearities, Phys. Rev. Lett. 91(12), 128101 (2003)
R. Stoop and A. Kern, Two-tone suppression and combination tone generation as computations performed by the hopf cochlea, Phys. Rev. Lett. 93(26), 8103 (2004)
K. Dierkes, B. Lindner, and F. Jüicher, Enhancement of sensitivity gain and frequency tuning by coupling of active hair bundles, Proc. Natl. Acad. Sci. USA 105(48), 18669 (2008)
A. Vilfan, and T. Duke, Frequency clustering in spontaneous otoacoustic emissions from a Lizard’s ear, Biophys. J. 95(10), 4622 (2008)
M. Gelfand, O. Piro, M. O. Magnasco, and A. J. Hudspeth, Hudspeth a J. Interactions between hair cells shape spontaneous otoacoustic emissions in a model of the Tokay Gecko’s cochlea, PLoS One 5(6), e11116 (2010)
H. P. Wit and P. van Dijk, Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators? J. Acoust. Soc. Am. 132(2), 918 (2012)
Z. Liu, B. Li, and Y.-C. Lai, Enhancing mammalian hearing by a balancing between spontaneous otoacoustic emissions and spatial coupling, Europhys. Lett. 98(2), 20005 (2012)
G. A. Manley, Cochlear mechanisms from a phylogenetic viewpoint, Proc. Natl. Acad. Sci. USA 97(22), 11736 (2000)
C. Köppl, Morphology of the basilar papilla of the bobtail lizard Tiliqua rugosa, Hear. Res. 35(2–3), 209 (1988)
J. Gómez-Gardenes, S. Gómez, A. Arenas, and Y. Moreno, Explosive synchronization transitions in scalefree networks, Phys. Rev. Lett. 106(12), 128701 (2011)
I. Leyva, R. Sevilla-Escoboza, J. M. Buldú, I. Sendina- Nadal, J. Gomez-Gardenes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, and S. Boccaletti, Explosive first-order transition to synchrony in networked chaotic oscillators, Phys. Rev. Lett. 108(16), 168702 (2012)
P. Ji, T. K. D. Peron, P. J. Menck, F. A. Rodrigues, and J. Kurths, Cluster explosive synchronization in complex networks, Phys. Rev. Lett. 110(21), 218701 (2013)
X. Zhang, X. Hu, J. Kurths, and Z. Liu, Explosive synchronization in a general complex network, Phys. Rev. E 88(1), 010802 (2013)
I. Leyva, A. Navas, I. Sendina-Nadal, J. A. Almendral, J. M. Buldú, M. Zanin, D. Papo, and S. Boccaletti, Explosive transitions to synchronization in networks of phase oscillators, Sci. Rep. 3, 1281 (2013)
Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Basin of attraction determines hysteresis in explosive synchronization, Phys. Rev. Lett. 112(11), 114102 (2014)
X. Zhang, Y. Zou, S. Boccaletti, and Z. Liu, Explosive synchronization as a process of explosive percolation in dynamical phase space, Sci. Rep. 4, 5200 (2014)
X. Hu, S. Boccaletti, W. Huang, X. Zhang, Z. Liu, S. Guan, and C. H. Lai, Exact solution for first-order synchronization transition in a generalized Kuramoto model, Sci. Rep. 4, 7262 (2014)
X. Zhang, S. Boccaletti, S. Guan, and Z. Liu, Explosive synchronization in adaptive and multilayer networks, Phys. Rev. Lett. 114(3), 038701 (2015)
T. Qiu, Y. Zhang, J. Liu, H. Bi, S. Boccaletti, Z. Liu, and S. Guan, Landau damping effects in the synchronization of conformist and contrarian oscillators, Sci. Rep. 5, 18235 (2015)
P. C. Matthews, R. E. Mirollo, and S. H. Strogatz, Dynamics of a large system of coupled nonlinear oscillators, Physica D 52(2–3), 293 (1991)
C. Wang and N. Garnier, Continuous and discontinuous transitions to synchronization, arXiv: 1609.05584
J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77(1), 137 (2005)
P. D. Welsby, The 12, 24, or is it 26 cranial nerves? Postgrad. Med. J. 80(948), 602 (2004)
L. Fredrickson-Hemsing, S. Ji, R. Bruinsma, and D. Bozovic, Mode-locking dynamics of hair cells of the inner ear, Phys. Rev. E 86(2), 21915 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, CQ., Pumir, A., Garnier, N.B. et al. Explosive synchronization enhances selectivity: Example of the cochlea. Front. Phys. 12, 128901 (2017). https://doi.org/10.1007/s11467-016-0634-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11467-016-0634-x