Canards in piecewise-linear systems: explosions and super-explosions
2013 ◽
Vol 469
(2154)
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pp. 20120603
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Keyword(s):
We show that a planar slow–fast piecewise-linear (PWL) system with three zones admits limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive growth. Using phase-space compactification, we show that these quasi-canard cycles are strongly related to a bifurcation at infinity. Furthermore, we investigate a limiting case in which we show the existence of a continuum of canard homoclinic connections that coexist for a single-parameter value and with amplitude ranging from an order of ε to an order of 1, a phenomenon truly associated with the non-smooth character of this system and which we call super-explosion .
2021 ◽
Vol 496
(2)
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pp. 124818
2019 ◽
Vol 18
(3)
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pp. 1031-1054
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2013 ◽
Vol 14
(5)
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pp. 2002-2012
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2015 ◽
Vol 431
(1)
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pp. 529-544
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2019 ◽
Vol 39
(9)
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pp. 5275-5299
Keyword(s):
2021 ◽
Vol 31
(09)
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pp. 2150136
Keyword(s):
2007 ◽
Vol 17
(02)
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pp. 445-457
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2020 ◽
Vol 54
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pp. 103112
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Keyword(s):