Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 895785, 15 pages
http://dx.doi.org/10.1155/2010/895785
Research Article

Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions

1Department of Mathematics, “G. Castelnuovo”, University of Rome, “La Sapienza”, Piazzale Aldo Moro 2, 00185 Rome, Italy
2DiFarma, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 29 January 2010; Accepted 24 March 2010

Academic Editor: Ming Li

Copyright © 2010 Gianni Mattioli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. El Boustani, M. Pospischil, M. Rudolph-Lilith, and A. Destexhe, “Activated cortical states: experiments, analyses and models,” Journal of Physiology Paris, vol. 101, no. 1–3, pp. 99–109, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. R. Fitzhugh, “Impulses and physiological states in theoretical models of nerve membrane,” Biophysical Journal, vol. 1, pp. 455–466, 1961. View at Google Scholar
  3. N. V. Georgiev, “Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model,” Journal of Applied Mathematics, no. 8, pp. 397–407, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Guckenheimer and I. S. Labouriau, “Bifurcation of the Hodgkin and Huxley equations: a new twist,” Bulletin of Mathematical Biology, vol. 55, no. 5, pp. 937–952, 1993. View at Publisher · View at Google Scholar · View at Scopus
  5. B. Hassard, “Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon,” Journal of Theoretical Biology, vol. 71, no. 3, pp. 401–420, 1978. View at Google Scholar · View at MathSciNet
  6. A. L. Hodgkin and A. F. Huxley, “Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo,” The Journal of Physiology, vol. 116, pp. 449–472, 1952. View at Google Scholar
  7. A. L. Hodgkin and A. F. Huxley, “The components of membrane conductance in the giant axon of Loligo,” The Journal of Physiology, vol. 116, no. 4, pp. 473–496, 1952. View at Google Scholar
  8. A. L. Hodgkin and A. F. Huxley, “The dual effect of membrane potential on sodium conductance in the giant axon of Loligo,” The Journal of Physiology, vol. 116, pp. 497–506, 1952. View at Google Scholar
  9. J. Nagumo, S. Arimoto, and S. Yoshizawa, “An active pulse transmission line simulating nerve axon,” Proceedings of the IRE, vol. 50, no. 10, pp. 2061–2070, 1962. View at Google Scholar
  10. J. Rinzel and R. N. Miller, “Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations,” Mathematical Biosciences, vol. 49, no. 1-2, pp. 27–59, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Wang, L. Chen, and X. Fei, “Analysis and control of the bifurcation of Hodgkin-Huxley model,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 247–256, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Mattioli and M. Scalia, “Modelling hodgkin-huxley neurons interaction,” in Proceedings of the International Conference on Computational Science and Its Applications (ICCSA '09), vol. 5592 of Lecture Notes in Computer Science, pp. 745–751, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. C. Cattani and J. Rushchitsky, Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, vol. 74 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Hackensack, NJ, USA, 2007. View at MathSciNet
  14. C. Cattani, “Haar wavelet-based technique for sharp jumps classification,” Mathematical and Computer Modelling, vol. 39, no. 2-3, pp. 255–278, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet