Canards in piecewise-linear systems: explosions and super-explosions

Mathieu Desroches 1 Emilio Freire 2 John Hogan 3 Enrique Ponce 2 Phanikhrisna Thota 4
1 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
Inria Paris-Rocquencourt
2 Department of Applied Mathematics II [Sevilla]
3 Applied Nonlinear Mathematics [Bristol]
4 Design Analysis -ELYD [Airbus]
Abstract : 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.
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Submitted on : Monday, July 15, 2013 - 10:16:24 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM

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Mathieu Desroches, Emilio Freire, John Hogan, Enrique Ponce, Phanikhrisna Thota. Canards in piecewise-linear systems: explosions and super-explosions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2013, 469 (2154), pp.20120603. ⟨http://rspa.royalsocietypublishing.org/content/469/2154/20120603.abstract⟩. ⟨10.1098/rspa.2012.0603⟩. ⟨hal-00844799⟩

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