Nonlinear cooperation between fast and slow dynamics underlying different subthreshold resonances in olive neurons model

Runxia Wang; Yanbing Jia; Yuye Li; Runxia Wang; Yanbing Jia; Yuye Li

doi:10.3934/era.2025343

Electronic Research Archive

2025, Volume 33, Issue 12: 7763-7790. doi: 10.3934/era.2025343

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Nonlinear cooperation between fast and slow dynamics underlying different subthreshold resonances in olive neurons model

1.
Department of General Education, Wuxi University, Wuxi 214105, China
2.
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
3.
College of Mathematics and Computer Science, Chifeng University, Chifeng 024000, China

Received: 31 August 2025 Revised: 17 December 2025 Accepted: 18 December 2025 Published: 24 December 2025

Different subthreshold resonance patterns characterized by different amplitudes and frequencies are evoked from the resting potential of the medial superior olive neurons, playing important roles in sound localization. In the present paper, the conditions and nonlinear cooperation mechanisms between two ionic currents for the different patterns are obtained in a neuronal model. As the resting potential is close to the half-activation voltage of low threshold potassium current (I_KLT), simulation results of resonances match the experimental observations. For weak stimulation with small amplitude, slow hyperpolarization-activated cation current (I_H) is not activated, whereas fast IKLT is activated to mediate a common single resonance, exhibiting small amplitude with symmetry to the resting potential and high frequency for sound localization. For strong stimulation with large amplitude, IH is also activated to mediate a low frequency resonance and enhance the frequency of resonance mediated by IKLT for precise sound localization. Then, an uncommon phenomenon of double resonances appears, which exhibits large and non-symmetrical amplitude. The different resonances are well explained with the fast frequency response of I_KLT and slow response of IH. Interestingly and paradoxically, an oscillation not around its steady value appears at a high frequency of stimulation, since I_H is too slow to recover. If the time scale of two currents becomes approximate, the paradoxical oscillation disappears. Finally, for the double resonances, the phase trajectory is wide enough to cover a large part of nullclines with nonlinearity, resulting in large and asymmetrical amplitudes. For the single resonance with small and symmetrical amplitude, the trajectory is narrow to cover only a local linear part of nullcline. These results present feasible measures to modulate the high frequency response of the medial superior olive neurons for sound localization.
- subthreshold resonance,
- double resonances,
- nullcline,
- sound localization,
- fast and slow response
Citation: Runxia Wang, Yanbing Jia, Yuye Li. Nonlinear cooperation between fast and slow dynamics underlying different subthreshold resonances in olive neurons model[J]. Electronic Research Archive, 2025, 33(12): 7763-7790. doi: 10.3934/era.2025343

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Abstract

Different subthreshold resonance patterns characterized by different amplitudes and frequencies are evoked from the resting potential of the medial superior olive neurons, playing important roles in sound localization. In the present paper, the conditions and nonlinear cooperation mechanisms between two ionic currents for the different patterns are obtained in a neuronal model. As the resting potential is close to the half-activation voltage of low threshold potassium current (I_KLT), simulation results of resonances match the experimental observations. For weak stimulation with small amplitude, slow hyperpolarization-activated cation current (I_H) is not activated, whereas fast IKLT is activated to mediate a common single resonance, exhibiting small amplitude with symmetry to the resting potential and high frequency for sound localization. For strong stimulation with large amplitude, IH is also activated to mediate a low frequency resonance and enhance the frequency of resonance mediated by IKLT for precise sound localization. Then, an uncommon phenomenon of double resonances appears, which exhibits large and non-symmetrical amplitude. The different resonances are well explained with the fast frequency response of I_KLT and slow response of IH. Interestingly and paradoxically, an oscillation not around its steady value appears at a high frequency of stimulation, since I_H is too slow to recover. If the time scale of two currents becomes approximate, the paradoxical oscillation disappears. Finally, for the double resonances, the phase trajectory is wide enough to cover a large part of nullclines with nonlinearity, resulting in large and asymmetrical amplitudes. For the single resonance with small and symmetrical amplitude, the trajectory is narrow to cover only a local linear part of nullcline. These results present feasible measures to modulate the high frequency response of the medial superior olive neurons for sound localization.

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