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

M. Desroches, E. Freire, S. J. Hogan, E. Ponce, P. Thota
2013 Proceedings of the Royal Society A  
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
more » ... 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.
doi:10.1098/rspa.2012.0603 fatcat:qhtoixn6zzdofbcuyi4uzc3s6y