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15-11-2021 | Research Article

Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state

Authors: Ben Cao, Huaguang Gu, Runxia Wang

Published in: Cognitive Neurodynamics | Issue 5/2022

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Abstract

The forced oscillations of hair bundle of inner hair cells of auditory nervous system evoked by external force from steady state are related to the fast adaption of hair cells, which are very important for auditory amplification. In the present paper, comprehensive and deep understandings to nonlinear dynamics of forced oscillations are acquired in four aspects. Firstly, the complex dynamics underlying the twitch (fast recoil of displacement X which is fast variable) induced from Case-1 and Case-2 steady states by external pulse force are obtained. With help of vector fields and nullclines, the phase trajectory of forced oscillations is identified to be an evolution process between two equilibrium points corresponding to zero force and pulse force, respectively, and then the twitch is obtained as the behavior running along the nonlinear part of X-nullcline. Especially, twitch observed in experiment are classified into 6 types, which are induced by negative change of force, negative and positive changes of force, and positive change of force, respectively, and further build relationships to three subcases of Case-2 steady state with N-shaped X-nullcline (equilibrium point locates on the left, middle, and right branches of X-nullcline, respectively). Secondly, the experimental observation of fatigue of twitch induced by continual two pulse forces, i.e. the reduced amplitude of the latter twitch when interval between two forces is short, is also explained as a nonlinear behavior beginning from an initial value different from that of the former one. Thirdly, the experimental observation of transition between sustained oscillations and steady state induced by pulse force can be simulated for Case-1 steady state with Z-shaped X-nullcline instead of Case-2, due to that there exists bifurcations with respect to external force for Case-1 while no bifurcations for Case-2. Last, the threshold phenomenon induced by simple pulse stimulation exists for Case-1 steady state rather than Case-2, due to that the upper and lower branches of Z-shaped X-nullcline close to the middle branch exhibit coexisting behaviors of variable X while N-shaped X-nullcline does not. The nonlinear dynamics of forced oscillations are helpful for explanations to the complex experimental observations, which presents potential measures to modulate the functions of twitch such as the fast adaption.

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Literature
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go back to reference Cao B, Gu H, Ma K (2021b) Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states. Cogn Neurodyn (submitted) Cao B, Gu H, Ma K (2021b) Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states. Cogn Neurodyn (submitted)
go back to reference Rong W, Wang R (2019) Neurodynamic Analysis of Cochlear Hair Cell Activity. Appl Math Mech(in Chinese) 40:139–149. https://doi.org/10.21656/1000-0887.390184 Rong W, Wang R (2019) Neurodynamic Analysis of Cochlear Hair Cell Activity. Appl Math Mech(in Chinese) 40:139–149. https://​doi.​org/​10.​21656/​1000-0887.​390184
Metadata
Title
Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state
Authors
Ben Cao
Huaguang Gu
Runxia Wang
Publication date
15-11-2021
Publisher
Springer Netherlands
Published in
Cognitive Neurodynamics / Issue 5/2022
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-021-09745-3

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