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

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Artificial Neural Networks: Biological Inspirations – ICANN 2005 (ICANN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3696))

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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. Rulkov, N.F.: Modeling of spiking-bursting neural behavior using two–dimensional map. Physical Review E 65, 41922 (2002)

    Article  MathSciNet  Google Scholar 

  2. Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. on Neural Networks 68, 052901 (2003)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Elson, R.C., et al.: Synchronous Behavior of Two Coupled biological Neurons. Physical Review Letters 81(25), 5692–5695 (1998)

    Article  Google Scholar 

  9. Izhikevich, E.M.: Neural Excitability, Spiking and Bursting. International Journal of Bifurcation and Chaos 10, 1171–1266 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Aguirre, C., Campos, D., Pascual, P., Serrano, E. (2005). Neuronal Behavior with Sub-threshold Oscillations and Spiking/Bursting Activity Using a Piecewise Linear Two-Dimensional Map. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Biological Inspirations – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550822_17

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  • DOI: https://doi.org/10.1007/11550822_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28752-0

  • Online ISBN: 978-3-540-28754-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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