title: Canard-like phenomena in piecewise-smooth Van der Pol systems.
abstract: We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard phenomena in nonlinear, piecewise-smooth systems can be qualitatively more similar to the phenomena in smooth systems than piecewise-linear systems, since the nonlinearity allows for canards to transition from small cycles to canards "with heads." The canards are born of a bifurcation that occurs as the slow-nullcline coincides with the splitting manifold. However, there are conditions under which this bifurcation leads to a phenomenon called super-explosion, the instantaneous transition from a globally attracting periodic orbit to relaxations oscillations. Also, we demonstrate that the bifurcation-whether leading to canards or super-explosion-can be subcritical.
authors.affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA.
authors.forename: Andrew
authors.initials: A
authors.lastname: Roberts
authors.affiliation: Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Paul
authors.initials: P
authors.lastname: Gendinning