Complex Dynamics of Nonlinear Oscillations of Hair Bundles of Auditory Hair Cell Regulated by Memristor

Ben Cao; Kai-Hua MA

doi:10.70693/cjst.v1i1.835

Authors

Ben Cao Nanjing University of Information Science and Technology https://orcid.org/0009-0000-9169-157X
Kai-Hua MA Jiangsu University of Technology

DOI:

https://doi.org/10.70693/cjst.v1i1.835

Keywords:

Nonlinear oscillation, Bifurcation, Hair cell, Memristor, Neuromodulation

Abstract

The nonlinear oscillations of hair bundles of auditory hair cell are important for sound perception. Memristors, as electronic components highly similar to the behavior of neurons and synapses, show potential in neuromodulation. The present paper, for the first time, introduces memristors into the regulation of hair bundle mechanical vibrations, constructs a dynamical model with memristor coupling, and investigates the regulatory dynamics of coupling strength (γ) on oscillation modes through simulation and bifurcation analysis. The results show that as γ increases, the hair bundle oscillation patterns exhibit a variety of complex patterns, including different types of spiking, bursting, and chaos. Bifurcation analysis and Lyapunov exponents validate the dynamic process of mode transitions, indicating that memristors influence oscillation patterns by regulating the adaptation force of hair bundle. Moreover, bifurcation analysis in the two-parameter plane indicates that increasing γ can expand the oscillation region of the hair bundle, but excessive coupling can suppress oscillations. Under specific parameter combinations, the system exhibits insensitivity to memristor regulation, reflecting the robustness of the auditory system. This study provides a theoretical basis for understanding the nonlinear characteristics of auditory function and developing novel neuromodulation technologies.

References

Hudspeth A J. Making an effort to listen: mechanical amplification in the ear[J]. Neuron, 2008, 59(4): 530-545. DOI: https://doi.org/10.1016/j.neuron.2008.07.012

Hudspeth A J. Integrating the active process of hair cells with cochlear function[J]. Nature Reviews Neuroscience, 2014, 15(9): 600-614. DOI: https://doi.org/10.1038/nrn3786

Hudspeth A J, Martin P. Evolving critical oscillators for hearing[J]. Nature Reviews Physics, 2024, 6(4): 210-211. DOI: https://doi.org/10.1038/s42254-023-00672-2

Szalai R, Tsaneva-Atanasova K, Homer M E, et al. Nonlinear models of development, amplification and compression in the mammalian cochlea[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011, 369(1954): 4183-4204. DOI: https://doi.org/10.1098/rsta.2011.0192

Fredrickson-Hemsing L, Strimbu C E, Roongthumskul Y, et al. Dynamics of freely oscillating and coupled hair cell bundles under mechanical deflection[J]. Biophysical Journal, 2012, 102(8): 1785-1792. DOI: https://doi.org/10.1016/j.bpj.2012.03.017

Ó Maoiléidigh D, Nicola E M, Hudspeth A J. The diverse effects of mechanical loading on active hair bundles[J]. Proceedings of the National Academy of Sciences of the United States of America, 2012, 109(6): 1943-1948. DOI: https://doi.org/10.1073/pnas.1120298109

Roongthumskul Y, Fredrickson-Hemsing L, Kao A, et al. Multiple-timescale dynamics underlying spontaneous oscillations of saccular hair bundles[J]. Biophysical Journal, 2011, 101(3): 603-610. DOI: https://doi.org/10.1016/j.bpj.2011.06.027

Benser M E, Marquis R E, Hudspeth A J. Rapid, active hair bundle movements in hair cells from the bullfrog’s sacculus[J]. Journal of Neuroscience, 1996, 16(18): 5629-5643. DOI: https://doi.org/10.1523/JNEUROSCI.16-18-05629.1996

Tinevez J Y, Jülicher F, Martin P. Unifying the various incarnations of active hair-bundle motility by the vertebrate hair cell[J]. Biophysical Journal, 2007, 93(11): 4053-4067. DOI: https://doi.org/10.1529/biophysj.107.108498

Lin C H J, Bozovic D. Effects of efferent activity on hair bundle mechanics[J]. Journal of Neuroscience, 2020, 40(12): 2390-2402. DOI: https://doi.org/10.1523/JNEUROSCI.1312-19.2020

Lin C H J, Bozovic D. Efferent activity controls hair cell response to mechanical overstimulation[J]. eNeuro, 2022, 9(4). DOI: https://doi.org/10.1523/ENEURO.0198-22.2022

Cao B, Gu H, Bai J, et al. Bifurcation and chaos of spontaneous oscillations of hair bundles in auditory hair cells[J]. International Journal of Bifurcation and Chaos, 2021, 31(4): 2130011. DOI: https://doi.org/10.1142/S0218127421300111

Cao B, Gu H, Ma K. Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states[J]. Cognitive Neurodynamics, 2022, 16(4): 917-940. DOI: https://doi.org/10.1007/s11571-021-09744-4

Cao B, Gu H, Wang R. Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state[J]. Cognitive Neurodynamics, 2021, 3(5): 1163-1188. DOI: https://doi.org/10.1007/s11571-021-09745-3

Khan W U, Shen Z, Mugo S M, et al. Implantable hydrogels as pioneering materials for next-generation brain–computer interfaces[J]. Chem Soc Rev, 2025. DOI: https://doi.org/10.1039/D4CS01074D

Xie Y, Ma J. How to discern external acoustic waves in a piezoelectric neuron under noise?[J]. Journal of Biological Physics, 2022, 48(3): 339-353. DOI: https://doi.org/10.1007/s10867-022-09611-1

Chua L O. Memristor—the missing circuit element[J]. IEEE Transactions on Circuit Theory, 1971, 18(5). DOI: https://doi.org/10.1109/TCT.1971.1083337

Shao Y, Wu F, Wang Q. Synchronization and complex dynamics in locally active threshold memristive neurons with chemical synapses[J]. Nonlinear Dynamics, 2024, 112(15): 13483-13502. DOI: https://doi.org/10.1007/s11071-024-09747-w

Wu F, Gu H, Jia Y. Bifurcations underlying different excitability transitions modulated by excitatory and inhibitory memristor and chemical autapses[J]. Chaos, Solitons and Fractals, 2021, 153: 111611. DOI: https://doi.org/10.1016/j.chaos.2021.111611

Wu F, Gu H. Bifurcations of negative responses to positive feedback current mediated by memristor in a neuron model with bursting patterns[J]. International Journal of Bifurcation and Chaos, 2020, 30(4): 1-22. DOI: https://doi.org/10.1142/S0218127420300098

Wu F, Gu H, Li Y. Inhibitory electromagnetic induction current induces enhancement instead of reduction of neural bursting activities[J]. Communications in Nonlinear Science and Numerical Simulation, 2019, 79: 104924. DOI: https://doi.org/10.1016/j.cnsns.2019.104924

Amin Fida A, Khanday F A, Mittal S. An active memristor based rate-coded spiking neural network[J]. Neurocomputing, 2023, 533: 61-71. DOI: https://doi.org/10.1016/j.neucom.2023.02.038

Zhou W, Jin P, Dong Y, et al. Memristor neurons and their coupling networks based on Edge of Chaos Kernel[J]. Chaos, Solitons and Fractals, 2023, 177: 114224. DOI: https://doi.org/10.1016/j.chaos.2023.114224

Bao B, Hu J, Bao H, et al. Memristor-coupled dual-neuron mapping model: initials-induced coexisting firing patterns and synchronization activities[J]. Cognitive Neurodynamics, 2024, 18(2): 539–555. DOI: https://doi.org/10.1007/s11571-023-10006-8

Ying J, Min F, Wang G. Neuromorphic behaviors of VO2 memristor-based neurons[J]. Chaos, Solitons and Fractals, 2023, 175: 114058. DOI: https://doi.org/10.1016/j.chaos.2023.114058

Roongthumskul Y, Faber J, Bozovic D. Dynamics of mechanically coupled hair-cell bundles of the inner ear[J]. Biophysical Journal, 2021, 120(2): 205-216. DOI: https://doi.org/10.1016/j.bpj.2020.11.2273

Martin P, Hudspeth A J. Compressive nonlinearity in the hair bundle’s active response to mechanical stimulation[J]. Proceedings of the National Academy of Sciences of the United States of America, 2001, 98(25): 14386-14391. DOI: https://doi.org/10.1073/pnas.251530498

Kim K J, Ahn K H. Amplitude death of coupled hair bundles with stochastic channel noise[J]. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2014, 89(4): 1-7. DOI: https://doi.org/10.1103/PhysRevE.89.042703

Yu X, Bao H, Xu Q, et al. Deep brain stimulation and lag synchronization in a memristive two-neuron network[J]. Neural Networks, 2024, 180: 106728. DOI: https://doi.org/10.1016/j.neunet.2024.106728

Zhang X, Li C, Iu H H C, et al. A chaotic memristive Hindmarsh-Rose neuron with hybrid offset boosting[J]. Chaos, Solitons and Fractals, 2024, 185: 115150. DOI: https://doi.org/10.1016/j.chaos.2024.115150

Bard E. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students[M]. Philadelphia: SIAM, 2002.