| Issue |
Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011
Instability and patterns. Issue dedicated to the memory of A. Golovin
|
|
|---|---|---|
| Page(s) | 149 - 162 | |
| DOI | https://doi.org/10.1051/mmnp/20116108 | |
| Published online | 09 June 2010 | |
On Chaotic Subthreshold Oscillations in a Simple Neuronal Model
Institute of Physics, Humboldt University of Berlin, D-12489,
Germany
* Corresponding author. E-mail:
zaks@physik.hu-berlin.de
In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
Mathematics Subject Classification: 92C20 / 37G15 / 34D15
Key words: slow-fast equations / period-doubling bifurcation
© EDP Sciences, 2010
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