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slow-fast equations

Mathematical Modelling of Natural Phenomena (1)

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On Chaotic Subthreshold Oscillations in a Simple NeuronalModel
M. Zaks
Journal:

Mathematical Modelling of Natural Phenomena / Volume 6 / Issue 1 / 2011

Published online by Cambridge University Press:

09 June 2010, pp. 149-162

Print publication:

2011
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In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, asequence of period-doubling bifurcations for small-scale oscillations precedes thetransition into the spiking regime. For a wide range of values of the timescale separationparameter, this scenario is recovered numerically. Its relation to the singularlyperturbed integrable system is discussed.