Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 895785, 15 pages
doi:10.1155/2010/895785
Research Article

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

Gianni Mattioli,1 Massimo Scalia,1 and Carlo Cattani2

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.

Abstract

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude (time-dependent) pulse. The corresponding numerical solution for some given values of parameters are analyzed through the wavelet coefficients, showing both the sensitivity to local jumps and some unexpected inertia of neuron's as response to the high-amplitude spike.