Journal article
Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models
In this work we consider a general class of 2-dimensional hybrid systems. Assuming that the system possesses an attracting equilibrium point, we show that, when periodically driven with a square-wave pulse, the system possesses a periodic orbit which may undergo smooth and nonsmooth grazing bifurcations.
We perform a semi-rigorous study of the existence of periodic orbits for a particular model consisting of a leaky integrate-and fire model with a dynamic threshold. We use the stroboscopic map, which in this context is a 2-dimensional piecewise-smooth discontinuous map. For some parameter values we are able to show that the map is a quasi-contraction possessing a (locally) unique maximin periodic orbit.
We complement our analysis using advanced numerical techniques to provide a complete portrait of the dynamics as parameters are varied. We find that for some regions of the parameter space the model undergoes a cascade of gluing bifurcations, while for others the model shows multistability between orbits of different periods.
Language: | English |
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Year: | 2019 |
Pages: | 48-73 |
ISSN: | 18787274 and 10075704 |
Types: | Journal article |
DOI: | 10.1016/j.cnsns.2018.09.006 |
ORCIDs: | Granados, Albert |