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Firing Pattern Estimation of Synaptically Coupled Hindmarsh-Rose Neurons by Adaptive Observer

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Artificial Neural Networks - ICANN 2008 (ICANN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5164))

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Abstract

In this paper, we present adaptive observers for synaptically coupled Hindmarsh-Rose(HR) neurons with the membrane potential measurement under the assumption that some of parameters in an individual HR neuron are known. Using the adaptive observers for a single HR neuron, we propose a two-stage merging procedure to identify the firing pattern of a model of synaptically coupled HR neurons. The procedure allows us to recover the internal states and to distinguish the firing patterns of the synaptically coupled HR neurons, with early-time dynamic behaviors.

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References

  1. Belykh, I., de Lange, E., Hasler, M.: Synchronization of bursting neurons: What matters in the network topology. Phys. Rev. Lett. 94, 188101 (2005)

    Article  Google Scholar 

  2. Izhikevich, E.M.: Which model to use for cortical spiking neurons? IEEE Trans on Neural Networks 15(5), 1063–1070 (2004)

    Article  Google Scholar 

  3. Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans on Neural Networks 14(6), 1569–1572 (2002)

    Article  Google Scholar 

  4. Hindmarsh, J., Rose, R.: A model of the nerve impulse using two first order differential equations. Nature 296, 162–164 (1982)

    Article  Google Scholar 

  5. Hindmarsh, J., Rose, R.: A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B. 221, 87–102 (1984)

    Article  Google Scholar 

  6. Carroll, T.L.: Chaotic systems that are robust to added noise. CHAOS 15, 013901 (2005)

    Article  Google Scholar 

  7. Arena, P., Fortuna, L., Frasca, M., Rosa, M.L.: Locally active Hindmarsh-Rose neurons. Chaos, Soliton and Fractals 27, 405–412 (2006)

    Article  MATH  Google Scholar 

  8. Meunier, N., Narion-Poll, R., Lansky, P., Rospars, J.O.: Estimation of the individual firing frequencies of two neurons recorded with a single electrode. Chem. Senses 28, 671–679 (2003)

    Article  Google Scholar 

  9. Tokuda, I., Parlitz, U., Illing, L., Kennel, M., Abarbanel, H.: Parameter estimation for neuron models. In: Proc. of the 7th Experimental Chaos Conference (2002)

    Google Scholar 

  10. Steur, E.: Parameter estimation in Hindmarsh-Rose neurons,traineeship report (2006), http://alexandria.tue.nl/repository/books/626834.pdf

  11. Marino, R.: Adaptive observers for single output nonlinear systems. IEEE Trans. on Automatic Control 35(9), 1054–1058 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  12. Mitsunaga, K., Totoki, Y., Matsuo, T.: Firing pattern estimation of biological neuron models by adaptive observer. In: Ishikawa, M., et al. (eds.) ICONIP 2007, Part I. LNCS, vol. 4984, pp. 83–92. Springer, Heidelberg (2008)

    Google Scholar 

  13. Narendra, K., Annaswamy, A.: Stable Adaptive Systems. Prentice Hall Inc., Englewood Cliffs (1989)

    Google Scholar 

  14. Katayama, K., Horiguchi, T.: Synchronous phenomena of neural network models using Hindmarsh-Rose equation. Interdisciplinary Information Sciences 11(1), 11–15 (2005)

    MATH  Google Scholar 

  15. Watts, L.: A tour of neuralog and spike - tools for simulating networks of spiking neurons (1993), http://www.lloydwatts.com/SpikeBrochure.pdf

  16. Yoden, S., Nomura, M.: Finite-time Lyapunov stability analysis and its application to atmospheric predictability. Journal of the Atmospheric Sciences 51(11), 1531–1543 (1993)

    Article  MathSciNet  Google Scholar 

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Véra Kůrková Roman Neruda Jan Koutník

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Totoki, Y., Mitsunaga, K., Suemitsu, H., Matsuo, T. (2008). Firing Pattern Estimation of Synaptically Coupled Hindmarsh-Rose Neurons by Adaptive Observer. In: Kůrková, V., Neruda, R., Koutník, J. (eds) Artificial Neural Networks - ICANN 2008. ICANN 2008. Lecture Notes in Computer Science, vol 5164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87559-8_35

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  • DOI: https://doi.org/10.1007/978-3-540-87559-8_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87558-1

  • Online ISBN: 978-3-540-87559-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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