Limit cycles, noise, and chaos in hearing

Stoop, Ruedi; Vyver, J.-J. van der; Kern, A.

doi:10.1002/jemt.20055

Cited by 7 publications

(6 citation statements)

References 32 publications

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“…Occasionally, mosquito antennae undergo spontaneous self-oscillations (6) that, in phase space, trace out an ellipse and are therefore quasisinusoidal (Fig. 3); this is in contrast to the limit cycles of, say, Drosophila, whose antennal limit cycle is of a relaxation type (20). Systems with limit cycles that are quasisinusoidal are practically equivalent to linear oscillators with weak nonlinear perturbations, and as such, the mosquito antennal auditory system can be considered to be weakly nonlinear (12).…”

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confidence: 99%

Synchrony through twice-frequency forcing for sensitive and selective auditory processing

Jackson

Windmill

Pook

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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Male mosquitoes detect flying females using antennal hearing organs sensitive to nanoscale mechanical displacements and that harbor motile mechanosensory neurons. The mechanisms supporting neuronal motility, and their function in peripheral sensory processing, remain, however, puzzling. The mechanical and neural responses reveal a transition that unmasks the onset of synchronization between sensory neurons. This synchronization constitutes an unconventional, mechanically driven, process of communication between sensory neurons. Enhancing auditory sensitivity and selectivity, synchronization between mechanosensors in the mosquito arises from entrainment to twice-frequency forcing and is formally analogous to injection-locking in high-power laser technology. This discovery opens up the enticing possibility that other sensory systems, even nonsensory cell ensembles, coordinate their actions through mechanical signaling.bioacoustics ͉ entrainment ͉ mosquito audition ͉ nonlinear hearing H earing organs convert acoustic energy into mechanical energy that, in turn, is transduced into action potentials from mechanically sensitive neurons. One particular challenge associated with this process is the extremely low energy content of sound waves. Physically, the sound energy imparted to the ear is weak, even compared with that conveyed by photons onto the retina of visual animals. In effect, energy thresholds for hearing can be close to thermal noise (Ϸ4 zJ), or one-hundredth of the energy of 1 single green photon (1, 2). Hearing has long been suggested, first by Gold (3), to operate in analogy to a regenerative amplifier, whereby the mechanically sensitive cells add their own mechanical energy to the oscillation they sense in the first place. Known as the cochlear amplifier in mammals and humans, this process assists sound-induced vibrations to nonlinearly amplify weak sounds and enhance frequency selectivity (4). Hearing organs usually comprise a large collection of mechanosensory cells (neurons in insects, epithelial hair cells in vertebrates) that can be viewed as an ensemble of mechanically coupled sensors. In mosquitoes and flies, auditory neurons have an unconventional dual sensory and motor function (5, 6) that is used to generate power, actively enhancing the mechanical response of the antenna to sound (5, 6).More generally, coupled nonlinear oscillators undergo a variety of synchronization phenomena (7,8), examples of which include fireflies flashing in unison (9) and chemical waves in the Belousov-Zhabotinsky (BZ) chemical reaction (10,11). Of particular importance is the class of synchronization called frequency entrainment (12), where coupled oscillators lock to the rhythm of an external stimulus. For example the suprachiasmatic nucleus of mammals, which controls circadian rhythms, is entrained to the day-night cycle by photoreceptors in the eye (7, 13). Further examples, borrowed from technology, include van der Pol's early investigations into entrainment of triode generators (14), and the synchronization of m...

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confidence: 99%

Synchrony through twice-frequency forcing for sensitive and selective auditory processing

Jackson

Windmill

Pook

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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“…37,38 Chaos may also be responsible for the anti-reliability of neurons. 22,39 However, in the present work, we have demonstrated that chaos is beneficial to sensory detection by hair cells. The dynamic state of a chaotic system depends sensitively on its initial conditions, and hence a small perturbation can result in a drastic change in the subsequent dynamics.…”

Section: Discussionmentioning

confidence: 45%

“…For example, a chaotic heartbeat is an indicator of cardiac fibrillation 39,40 . Chaos may also be responsible for the anti-reliability of neurons 24,41 . However, in the present work, we have demonstrated that chaos is beneficial to sensory detection by hair cells.…”

Section: Discussionmentioning

confidence: 99%

Chaotic Dynamics Enhance the Sensitivity of Inner Ear Hair Cells

Faber

Bozovic

2019

Sci Rep

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Hair cells of the auditory and vestibular systems are capable of detecting sounds that induce sub-nanometer vibrations of the hair bundle, below the stochastic noise levels of the surrounding fluid. Furthermore, the auditory system exhibits a highly rapid response time, in the sub-millisecond regime. We propose that chaotic dynamics enhance the sensitivity and temporal resolution of the hair bundle response, and we provide experimental and theoretical evidence for this effect. We use the Kolmogorov entropy to measure the degree of chaos in the system and the transfer entropy to quantify the amount of stimulus information captured by the detector. By varying the viscosity and ionic composition of the surrounding fluid, we are able to experimentally modulate the degree of chaos observed in the hair bundle dynamics in vitro. We consistently find that the hair bundle is most sensitive to a stimulus of small amplitude when it is poised in the weakly chaotic regime. Further, we show that the response time to a force step decreases with increasing levels of chaos. These results agree well with our numerical simulations of a chaotic Hopf oscillator and suggest that chaos may be responsible for the high sensitivity and rapid temporal response of hair cells.

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“…Physiological evidence exists for this active audition due to Hopf bifurcations for a range of animals and insect auditory systems [8][9][10][11]. Models have also been proposed which make use of coupling between limit cycles, which result from Hopf bifurcations, to produce significant amplification in insect hearing [12,13].…”

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confidence: 99%

Sensitive Signal Detection Using a Feed-Forward Oscillator Network

2007

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We present the results of an experimental investigation of a network of nonlinear coupled oscillators which are coupled in feed-forward mode. By exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point, we have found remarkable amplification of small signals over a narrow bandwidth with a large dynamic range. The effect is exploited to extract a small amplitude periodic signal from an input time series which is dominated by noise. Specifically, we have used this relatively simple experimental system to measure responses with a bandwidth of approximately 1% of the central frequency, amplifications of approximately 60 dB, and a dynamic range of approximately 80 dB and can extract signals from a time series with a signal to noise ratio of approximately -50 dB.

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Limit cycles, noise, and chaos in hearing

Cited by 7 publications

References 32 publications

Synchrony through twice-frequency forcing for sensitive and selective auditory processing

Synchrony through twice-frequency forcing for sensitive and selective auditory processing

Chaotic Dynamics Enhance the Sensitivity of Inner Ear Hair Cells

Sensitive Signal Detection Using a Feed-Forward Oscillator Network

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