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Canards in piecewise-linear systems: explosions and super-explosions
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.
https://hal.inria.fr/hal-00844799
Contributor : Mathieu Desroches <>
Submitted on : Monday, July 15, 2013 - 10:16:24 PM
Last modification on : Thursday, January 7, 2021 - 3:26:17 PM
Contributor : Mathieu Desroches <>
Submitted on : Monday, July 15, 2013 - 10:16:24 PM
Last modification on : Thursday, January 7, 2021 - 3:26:17 PM
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