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Zbl 1189.37099
Mattioli, Gianni; Scalia, Massimo; Cattani, Carlo
Analysis of large-amplitude pulses in short time intervals: application to neuron interactions. (English)
[J] Math. Probl. Eng. 2010, Article ID 895785, 15 p. (2010). ISSN 1024-123X; ISSN 1563-5147/e

Summary: 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.

MSC 2000:: *37N25 Dynamical systems in biology
92B20 General theory of neural networks

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