Limit cycles, noise, and chaos in hearing

Based on insight obtained from a newly developed cochlea model, we argue that noise‐driven limit cycles are the basic ingredient in the mammalian cochlea hearing process. For insect audition, we provide evidence in favor of the persistence of this principle. We emphasize the role of bifurcations for the emergence of broad‐range sound perception, both in the frequency and amplitude domain, and indicate that this crucially depends on the correct coupling between limit cycles. We review the limit‐cycle coupling universality, and outline how it can be used to encode information. Cortical noise is the microscopic basis for this encoding, whereas chaos emerges as the macroscopic expression of computation being done in the network. Large neuron firing variability is one possible consequence of the proposed mechanism that may apply to both vertebrate and insect hearing. Microsc. Res. Tech. 63:400–412, 2004. © 2004 Wiley‐Liss, Inc.

[1]  R. FitzHugh Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[2]  Kaspar Anton Schindler,et al.  When pyramidal neurons lock, when they respond chaotically, and when they like to synchronize , 2000, Neuroscience Research.

[3]  Thomas Gold,et al.  Hearing. II. The Physical Basis of the Action of the Cochlea , 1948, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[4]  Wiesenfeld,et al.  Period-doubling systems as small-signal amplifiers. , 1985, Physical review letters.

[5]  M. Ruggero Responses to sound of the basilar membrane of the mammalian cochlea , 1992, Current Opinion in Neurobiology.

[6]  R. Fettiplace,et al.  An electrical tuning mechanism in turtle cochlear hair cells , 1981, The Journal of physiology.

[7]  P. Coleman,et al.  Experiments in hearing , 1961 .

[8]  James Lighthill,et al.  Energy flow in the cochlea , 1981, Journal of Fluid Mechanics.

[9]  Malvin C. Teich,et al.  Fractal neuronal firing patterns , 1992 .

[10]  Ruedi Stoop,et al.  Encounter with Chaos , 1992 .

[11]  E. D. Boer,et al.  Auditory physics. Physical principles in hearing theory. III , 1984 .

[12]  John P. Miller,et al.  Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance , 1996, Nature.

[13]  C. Daniel Geisler,et al.  A cochlear model using feed-forward outer-hair-cell forces , 1995, Hearing Research.

[14]  L. Goddard Information Theory , 1962, Nature.

[15]  R Stoop,et al.  Stochastic resonance in pattern recognition by a holographic neuron model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Professor Moshe Abeles,et al.  Local Cortical Circuits , 1982, Studies of Brain Function.

[17]  D. Robert,et al.  The Evolutionary Innovation of Tympanal Hearing in Diptera , 1998 .

[18]  SEDLEY TAYLOR,et al.  Die Lehre von den Tonempfindimgen , 1871, Nature.

[19]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[20]  D. Kemp Stimulated acoustic emissions from within the human auditory system. , 1978, The Journal of the Acoustical Society of America.

[21]  Thomas Gold,et al.  Hearing , 1953, Trans. IRE Prof. Group Inf. Theory.

[22]  Michael N. Shadlen,et al.  Noise, neural codes and cortical organization , 1994, Current Opinion in Neurobiology.

[23]  A. Hudspeth,et al.  Essential nonlinearities in hearing. , 2000, Physical review letters.

[24]  Kaspar Anton Schindler,et al.  Neocortical networks of pyramidal neurons: from local locking and chaos to macroscopic chaos and synchronization , 2000 .

[25]  Grebogi,et al.  Unstable periodic orbits and the dimensions of multifractal chaotic attractors. , 1988, Physical review. A, General physics.

[26]  M. Feigenbaum Quantitative universality for a class of nonlinear transformations , 1978 .

[27]  Robert Patuzzi,et al.  Cochlear Micromechanics and Macromechanics , 1996 .

[28]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[29]  R. Douglas,et al.  An intracellular study of the contrast-dependence of neuronal activity in cat visual cortex. , 1997, Cerebral cortex.

[30]  J. Guckenheimer,et al.  Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos , 1991 .

[31]  G. Békésy,et al.  Experiments in Hearing , 1963 .

[32]  Michael C. Mackey,et al.  From Clocks to Chaos , 1988 .

[33]  A J Hudspeth,et al.  Comparison of a hair bundle's spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Brun,et al.  Period-doubling lasers as small-signal detectors. , 1985, Physical review letters.

[35]  M. Göpfert,et al.  Motion generation by Drosophila mechanosensory neurons , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Markus Christen,et al.  Collective bursting in layer IV. Synchronization by small thalamic inputs and recurrent connections. , 2002, Brain research. Cognitive brain research.