Synchronization of Ghostburster Neurons under External Electrical Stimulation: An Adaptive Approach

  • Wei Wei
  • Dong Hai Li
  • Jing Wang
  • Min Zhu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 97)

Abstract

The synchronization of two Ghostburster neurons under different external electrical stimulations is considered. Firstly, the periodic and chaotic dynamical behaviors of single Ghostburster neuron under various external electrical stimulations are analysed. Then the synchronization of general master-slave chaotic systems is formulated and an adaptive controller based dynamic compensation is designed to synchronize two Ghostburster neurons. Since the adaptive controller based on dynamic compensation is utilized, the exact knowledge of the systems is not necessarily required. Asymptotic synchronization can be achieved by choosing proper controller parameters. Simulation results confirm that the adaptive control approach employed in this paper is valid in the synchronization of two Ghostburster neurons.

Keywords

synchronization Ghostburster neurons adaptive control dynamic compensation 

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References

  1. 1.
    Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A universal Concept in Nonlinear Sciences. Cambridge University Press, New York (2001)CrossRefGoogle Scholar
  2. 2.
    Womelsdorf, T., Fries, P.: The role of neuronal synchronization in selective attention. Curr. Opin. Neurobiol. 17(2), 154–160 (2007)CrossRefPubMedGoogle Scholar
  3. 3.
    Gray, C.M.: Synchronous oscillations in neuronal systems: Mechanisms and functions. J. Comput. Neurosci. 1, 11–38 (1994)CrossRefPubMedGoogle Scholar
  4. 4.
    Basar, E.: Brain Function and Oscillations I: Brain oscillations, Principles and Approaches. Springer, Berlin (1998)CrossRefGoogle Scholar
  5. 5.
    Haken, H.: Branin Dynamics-Synchronization and Activity Patterns in Pulse-Coupled Neural Nets with Delays and Noise. Springer, Berlin (2002)Google Scholar
  6. 6.
    Gray, C.M., König, P., Engel, A.K., Singer, W.: Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338, 334–337 (1989)CrossRefPubMedGoogle Scholar
  7. 7.
    Gray, C.M., Mcormick, D.A.: Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronization oscillations in the visual cortex. Science 274, 109–113 (1996)CrossRefPubMedGoogle Scholar
  8. 8.
    Wang, Q.Y., Duan, Z.S., Feng, Z.S., Chen, G.R., Lu, Q.S.: Synchronization transition in gap-junction-coupled leech neurons. Physica A 387, 4404–4410 (2008)CrossRefGoogle Scholar
  9. 9.
    Meister, M., Wong, R.O., Baylor, D.A., Shatz, C.J.: Synchronous bursts of action potentials in ganglion cells of the developing mammalian retina. Science 252, 939–943 (1991)CrossRefPubMedGoogle Scholar
  10. 10.
    Kreiter, A.K., Singer, W.: Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey. J. Neurosci. 16, 2381–2396 (1996)PubMedGoogle Scholar
  11. 11.
    Che, Y.Q., Wang, J., Tsang, K.M., Chan, W.L.: Unidirectional synchronization for Hindmarsh-Rose neurons via robust adaptive sliding mode control. Nonlinear Analysis: Real World Applications 11, 1096–1104 (2010)CrossRefGoogle Scholar
  12. 12.
    Shuai, J.W., Durand, D.M.: Phase synchronization in two coupled chaotic neurons. Phys. Lett. A 264, 289–297 (1999)CrossRefGoogle Scholar
  13. 13.
    Hodgkin, L., Huxley, A.F.: A quantitative description of membrane and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    FitzhHugh, R.: Trashholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol. 43, 867–896 (1960)CrossRefGoogle Scholar
  15. 15.
    Hindmarsh, J.L., Rose, R.M.: A model of neuronal busting using three coupled first order differential equations. Proc. Roy. Soc. Lond. B Biol. 221, 87–102 (1984)CrossRefGoogle Scholar
  16. 16.
    Chay, T.R.: Chaos in a three-variable model of an excitable cell. Physica D 16, 233–242 (1985)CrossRefGoogle Scholar
  17. 17.
    Morris, C., Lecar, H.: Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35, 193–213 (1981)CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Shilnikov, A., Calabrese, R.L., Cymbalyuk, G.: Mechanism of bistability: Tonic spiking and bursting in a neuron model. Phys. Rev. E 71 (2005), 056214-9Google Scholar
  19. 19.
    Doiron, B., Laing, C., Longtin, A.: Ghostbursting : a novel neuronal burst mechanism. J. Comput. Neurosci. 12, 5–25 (2002)CrossRefPubMedGoogle Scholar
  20. 20.
    Cornejo-Pérez, O., Femat, R.: Unidirectional synchronization of Hodgkin-Huxley neurons. Chaos, Solitons and Fractals 25, 43–53 (2005)CrossRefGoogle Scholar
  21. 21.
    Wang, J., Zhang, T., Deng, B.: Synchronization of FitzHugh-Nagumo neurons in external electrical stimulation via nonlinear control. Chaos, Solitons and Fractals 31, 30–38 (2007)CrossRefGoogle Scholar
  22. 22.
    Zhang, T., Wang, J., Fei, X.Y., Deng, B.: Synchronization of coupled FitzHugh-Nagumo systems via MIMO feedback linearization control. Chaos, Solitons and Fractals 33, 194–202 (2007)CrossRefGoogle Scholar
  23. 23.
    Aguilar-López, R., Martínez-Guerra, R.: Synchronization of a coupled Hodgkin-Huxley neurons via high order sliding-mode feedback. Chaos, Solitons and Fractals 37, 539–546 (2008)CrossRefGoogle Scholar
  24. 24.
    Wang, J., Che, Y.Q., Zhou, S.S., Deng, B.: Unidirectional synchronization of Hodgkin-Huxley neurons exposed to ELF electric field. Chaos, Solitons and Fractals 39, 1335–1345 (2009)CrossRefGoogle Scholar
  25. 25.
    Ahmet, U., Lonngren, K.E., Bai, E.W.: Synchronization of the coupled FitzHugh-Nagumo systems. Chaos, Solitons and Fractals 20, 1085–1090 (2004)CrossRefGoogle Scholar
  26. 26.
    Wei, X.L., Wang, J., Deng, B.: Introducing internal model to robust output synchronization of FitzHugh-Nagumo neurons in external electrical sitmulation. Commu. Nonlinear Sci. Numer. Simulat. 14, 3108–3119 (2009)CrossRefGoogle Scholar
  27. 27.
    Deng, B., Wang, J., Fei, X.Y.: Synchronization two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solitons and Fractals 29, 182–189 (2006)CrossRefGoogle Scholar
  28. 28.
    Li, H.Y., Wong, Y.K., Chan, W.L., Tsang, K.M.: Synchronization of Ghostburster neurons under external electrical stimulation via adaptive neural network H ∞  control. Neurocomputing (2010), doi:10.1016/j.neucom.2010.03.004Google Scholar
  29. 29.
    Wu, Q.J., Zhou, J., Xiang, L., Liu, Z.R.: Impulsive control and synchronization of chaotic Hindmarsh-Rose models for neuronal activity. Chaos, Solitons and Fractals 41, 2706–2715 (2009)CrossRefGoogle Scholar
  30. 30.
    Laing, C.R., Doiron, B., Longtin, A., Maler, L.: Ghostbursting: the effects of dendrites on spike patterns. Neurocomputing 44-46, 127–132 (2002)CrossRefGoogle Scholar
  31. 31.
    Oswald, A.M., Chacron, M.J., Doiron, B., et al.: Parallel processing of sensory input by bursts and isolated spikes. The Journal of Neuroscience 24(18), 4351–4362 (2004)CrossRefPubMedGoogle Scholar
  32. 32.
    Wang, J., Chen, L., Deng, B.: Synchronization of Ghostburster neuron in external electrical stimulation via H ∞  variable universe fuzzy adaptive control. Chaos, Solitons and Fractals 39, 2076–2085 (2009)CrossRefGoogle Scholar
  33. 33.
    Sun, L., Wang, J., Deng, B.: Global synchronization of two Ghostburster neurons via active control. Chaos, Solitons and Fractals 40, 1213–1220 (2009)CrossRefGoogle Scholar
  34. 34.
    Tornambé, A., Valigi, P.: A decentralized controller for the robust stabilization of a class of MIMO dynamical systems. Journal of Dynamic Systems, Measurement and Control 116, 293–304 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Wei Wei
    • 1
  • Dong Hai Li
    • 2
  • Jing Wang
    • 3
  • Min Zhu
    • 4
  1. 1.School of Computer and Information EngineeringBeijing Technology and Business UniversityBeijingP.R. China
  2. 2.State Key Lab of Power Systems, Department of Thermal EngineeringTsinghua UniversityBeijingP.R. China
  3. 3.Institute of Engineering ResearchUniversity of Science and Technology BeijingBeijingP.R. China
  4. 4.Department of Thermal EngineeringTsinghua UniversityBeijingP.R. China

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