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

Mathieu Desroches | Zendy; E. Freire | Zendy; S. J. Hogan | Zendy; Enrique Ponce | Zendy; Phanikrishna Thota | Zendy

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

Author(s) -

Mathieu Desroches,

E. Freire,

S. J. Hogan,

Enrique Ponce,

Phanikrishna Thota

Publication year - 2013

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2012.0603

Subject(s) - homoclinic orbit , explosive material , parameter space , amplitude , piecewise linear function , mathematics , limiting , planar , bounding overwatch , mathematical analysis , bifurcation , nonlinear system , physics , computer science , geometry , quantum mechanics , engineering , mechanical engineering , chemistry , computer graphics (images) , organic chemistry , artificial intelligence

International audienceWe 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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