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Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models

Author
Granados, A.; Huguet, G.
Type of activity
Journal article
Journal
Communications in nonlinear science and numerical simulation
Date of publication
2019-05-01
Volume
70
First page
48
Last page
73
DOI
https://doi.org/10.1016/j.cnsns.2018.09.006 Open in new window
Repository
http://hdl.handle.net/2117/126893 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S1007570418302867 Open in new window
Abstract
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, ...
Citation
Granados, A., Huguet, G. Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models. "Communications in nonlinear science and numerical simulation", 1 Maig 2019, vol. 70, p. 48-73.
Keywords
Integrate-and-fire, hybrid systems, piecewise smooth 2d maps, quasi-contractions
Group of research
SD - UPC Dynamical Systems

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