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**Analysis of large-amplitude pulses in short time intervals: application to neuron interactions.**
*(English)*
Zbl 1189.37099

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:

37N25 | Dynamical systems in biology |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{G. Mattioli} et al., Math. Probl. Eng. 2010, Article ID 895785, 15 p. (2010; Zbl 1189.37099)

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