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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:
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)