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Phase-locking and chaos in a silent Hodgkin–Huxley neuron exposed to sinusoidal electric field

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  • Che, Yan-Qiu
  • Wang, Jiang
  • Si, Wen-Jie
  • Fei, Xiang-Yang

Abstract

Neuronal firing patterns are related to the information processing in neural system. This paper investigates the response characteristics of a silent Hodgkin–Huxley neuron to the stimulation of externally-applied sinusoidal electric field. The neuron exhibits both p:q phase-locked (i.e. a periodic oscillation defined as p action potentials generated by q cycle stimulations) and chaotic behaviors, depending on the values of stimulus frequencies and amplitudes. In one-parameter space, a rich bifurcation structure including period-adding without chaos and phase-locking alternated with chaos suggests frequency discrimination of the neuronal firing patterns. Furthermore, by mapping out Arnold tongues, we partition the amplitude–frequency parameter space in terms of the qualitative behaviors of the neuron. Thus the neuron’s information (firing patterns) encodes the stimulus information (amplitude and frequency), and vice versa.

Suggested Citation

  • Che, Yan-Qiu & Wang, Jiang & Si, Wen-Jie & Fei, Xiang-Yang, 2009. "Phase-locking and chaos in a silent Hodgkin–Huxley neuron exposed to sinusoidal electric field," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 454-462.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:454-462
    DOI: 10.1016/j.chaos.2007.03.008
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    References listed on IDEAS

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    1. Wang, Jiang & Zhang, Hua & Che, Yan-qiu, 2006. "Analysis of Hopf bifurcation caused by leakage conductance gl in the Hodgkin–Huxley model in muscles," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 427-436.
    2. He, Ji-Huan, 2006. "A modified Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 303-306.
    3. Jiang, Wang & Yanqiu, Che & Xiangyang, Fei & Li, Li, 2005. "Multi-parameter Hopf-bifurcation in Hodgkin–Huxley model exposed to ELF external electric field," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1221-1229.
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    1. Kesmia, Mounira & Boughaba, Soraya & Jacquir, Sabir, 2020. "Control of continuous dynamical systems modeling physiological states," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    2. Ding, Qianming & Wu, Yong & Hu, Yipeng & Liu, Chaoyue & Hu, Xueyan & Jia, Ya, 2023. "Tracing the elimination of reentry spiral waves in defibrillation: Temperature effects," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Hu Wang & Sha Wang & Yajuan Gu & Yongguang Yu, 2023. "Hopf Bifurcation Analysis of a Two-Dimensional Simplified Hodgkin–Huxley Model," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
    4. Bashkirtseva, Irina & Nasyrova, Venera & Ryashko, Lev, 2018. "Noise-induced bursting and chaos in the two-dimensional Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 76-81.
    5. Rosa, Cleiton & Correia, Marcos J. & Rech, Paulo C., 2009. "Arnold tongues and quasiperiodicity in a prey–predator model," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2041-2046.

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