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Chaos control and synchronization of two neurons exposed to ELF external electric field

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  • Wang, Jiang
  • Zhang, Ting
  • Che, Yanqiu

Abstract

Chaos control and synchronization of two unidirectional coupled neurons exposed to ELF electrical field via nonlinear control technique is investigated. Based on results of space–time characteristics of trans-membrane voltage, the variation of cell trans-membrane voltage exposed to extremely low frequency (ELF) electric field is analyzed. The dynamical behaviors of the modified Hodgkin–Huxley (HH) model are identified under the periodic ELF electric field using both analytical and numerical analysis. Then, using the results of the analysis, a nonlinear feedback linearization control scheme and a modified adaptive control strategy are designed to synchronize the two unidirectional coupled neurons and stabilize the chaotic trajectory of the slave system to desired periodic orbit of the master system. The simulation results demonstrated the efficiency of the proposed algorithms.

Suggested Citation

  • Wang, Jiang & Zhang, Ting & Che, Yanqiu, 2007. "Chaos control and synchronization of two neurons exposed to ELF external electric field," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 839-850.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:3:p:839-850
    DOI: 10.1016/j.chaos.2006.03.098
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    References listed on IDEAS

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    1. Cornejo-Pérez, Octavio & Femat, Ricardo, 2005. "Unidirectional synchronization of Hodgkin–Huxley neurons," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 43-53.
    2. Cao, Jinde & Li, H.X. & Ho, Daniel W.C., 2005. "Synchronization criteria of Lur’e systems with time-delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1285-1298.
    3. Fotsin, Hilaire & Bowong, Samuel & Daafouz, Jamal, 2005. "Adaptive synchronization of two chaotic systems consisting of modified Van der Pol–Duffing and Chua oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 215-229.
    4. 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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    Cited by:

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    3. Polynikis, A. & di Bernardo, M. & Hogan, S.J., 2009. "Synchronizability of coupled PWL maps," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1353-1367.
    4. Shang, Li-Jen & Shyu, Kuo-Kai, 2009. "A method for extracting chaotic signal from noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1120-1125.

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