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Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron

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  • Yilmaz, Ergin
  • Ozer, Mahmut

Abstract

We study the effect of the delayed feedback loop on the weak periodic signal detection performance of a stochastic Hodgkin–Huxley neuron. We consider an electrical autapse characterized by its coupling strength and delay time. The stochastic Hodgkin–Huxley neuron exhibits subthreshold oscillations, and thus has an intrinsic time scale with the subthreshold oscillations. Therefore, we investigate the interplay of the subthreshold oscillations, coupling strength and delay time on the weak periodic signal detection. Results indicate that the delayed feedback either enhances or suppresses the weak signal detection depending on its parameters, when compared to that without the feedback. The delayed feedback augments the weak periodic signal detection for the optimal values of the intrinsic noise and the coupling strength when the delay time is close to the integer multiples of the period of the intrinsic oscillations, due to the multiple resonance among the weak signal, the intrinsic oscillations, and the delayed feedback.

Suggested Citation

  • Yilmaz, Ergin & Ozer, Mahmut, 2015. "Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 455-462.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:455-462
    DOI: 10.1016/j.physa.2014.10.096
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    Citations

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    Cited by:

    1. Uzun, Rukiye & Yilmaz, Ergin & Ozer, Mahmut, 2017. "Effects of autapse and ion channel block on the collective firing activity of Newman–Watts small-world neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 386-396.
    2. Liu, Yaru & Liu, Shenquan & Zhan, Feibiao & Zhang, Xiaohan, 2020. "Firing patterns of the modified Hodgkin–Huxley models subject to Taylor ’s formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Wang, QiuBao & Yang, YueJuan & Zhang, Xing, 2020. "Weak signal detection based on Mathieu-Duffing oscillator with time-delay feedback and multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Yilmaz, Ergin & Baysal, Veli & Ozer, Mahmut & Perc, Matjaž, 2016. "Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 538-546.
    5. Chunni Wang & Shengli Guo & Ying Xu & Jun Ma & Jun Tang & Faris Alzahrani & Aatef Hobiny, 2017. "Formation of Autapse Connected to Neuron and Its Biological Function," Complexity, Hindawi, vol. 2017, pages 1-9, February.
    6. Ni Zhang & Dongxi Li & Yanya Xing, 2021. "Autapse-induced multiple inverse stochastic resonance in a neural system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-11, January.
    7. Baysal, Veli & Calim, Ali, 2023. "Stochastic resonance in a single autapse–coupled neuron," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    8. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    9. Yu, Haitao & Galán, Roberto F. & Wang, Jiang & Cao, Yibin & Liu, Jing, 2017. "Stochastic resonance, coherence resonance, and spike timing reliability of Hodgkin–Huxley neurons with ion-channel noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 263-275.
    10. Uzun, Rukiye, 2017. "Influences of autapse and channel blockage on multiple coherence resonance in a single neuron," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 203-210.

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