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Neuronal Behavior with Sub-threshold Oscillations and Spiking/Bursting Activity Using a Piecewise Linear Two-Dimensional Map

  • Carlos Aguirre
  • Doris Campos
  • Pedro Pascual
  • Eduardo Serrano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3696)

Abstract

A phenomenological neuronal model based on a coupled piecewise linear two–dimensional map is presented. The model mimics many of the neuronal features such as spiking, bursting and subthreshold activity. The model requires a computational effort lower than most of the phenomenological or differential neuronal models and its behavior is coherent with the one present in the other models. The regimes of synchronization of a pair of coupled maps is also explored.

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References

  1. 1.
    Rulkov, N.F.: Modeling of spiking-bursting neural behavior using two–dimensional map. Physical Review E 65, 41922 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. on Neural Networks 68, 052901 (2003)Google Scholar
  3. 3.
    Aguirre, C., Campos, D., Pascual, P., Serrano, E.: A model of spiking-bursting neuronal behavior using a piecewise linear two-dimensional map. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005. LNCS, vol. 3512, pp. 130–135. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and application to conduction and excitation in nerve. Journal of Physiology 117, 165–181 (1954)Google Scholar
  5. 5.
    Rose, R.M., Hindmarsh, J.L.: The assembly of ionic currents in a thalamic neuron, I The three dimensional model. Proceedings of The Royal Society of London B 237, 267–288 (1989)CrossRefGoogle Scholar
  6. 6.
    Makarov, V.A., Nekorkin, V.I., Velarde, M.G.: Spiking behavior in a noise-driven system combining oscillatory and excitatory properties. Physical Review Letters 86, 3431 (2001)CrossRefGoogle Scholar
  7. 7.
    Shilnikov, A.L., Rulkov, N.F.: Subthreshold oscillations in a map-based neuron model. Physics Letters A 328, 177–184 (2004)Google Scholar
  8. 8.
    Elson, R.C., et al.: Synchronous Behavior of Two Coupled biological Neurons. Physical Review Letters 81(25), 5692–5695 (1998)CrossRefGoogle Scholar
  9. 9.
    Izhikevich, E.M.: Neural Excitability, Spiking and Bursting. International Journal of Bifurcation and Chaos 10, 1171–1266 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Rulkov, N.F., Timofeev, I., Bazhenov, M.: Oscillations in large-scale cortical networks: map-based model Modeling of spiking-bursting neural behavior using two–dimensional map. J. Computational Neuroscience 17, 203–223 (2004)CrossRefGoogle Scholar
  11. 11.
    Bazhenov, M., Stopfer, M., Rabinovich, M., Huerta, R., Abarbanel, H.D.I., Sejnowski, T.J., Laurent, G.: Model of transient oscillatory synchronization in the locust antennal lobe. Neuron 30, 553–567 (2001)CrossRefGoogle Scholar
  12. 12.
    Gray, C.M., Singer, W.: Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proceedings of the National Academy of Sciences. U.S.A. 86, 1698–1702 (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carlos Aguirre
    • 1
  • Doris Campos
    • 1
  • Pedro Pascual
    • 1
  • Eduardo Serrano
    • 1
  1. 1.GNB, Escuela Politécnica SuperiorUniversidad Autonoma de MadridMadridSpain

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