Desroches, Mathieu F

Jeffrey, Mike R

Sudden changes in a dynamical system can be modelled by mixtures of slow and fasttimescales, or by combining smooth change with sudden switching. In sets of ordinarydiﬀerential equations, the former are modelled using singular perturbations, the latter usingdiscontinuities. The relation between the two is not well understood, and here we developa method called pinching, which approximates a singularly perturbed dynamical system bya discontinuous one, by making a discontinuous change of variables. We study pinching inthe context of the canard phenomenon at a folded node. The folded node is a singularityassociated with loss of normal hyperbolicity in slow-fast systems with (at least) two slowvariables, and canards are special solutions that characterize the local dynamics. Pinchingyields an approximation in terms of the two-fold singularity of discontinuous (Filippov)systems, which arises generically in three or more dimensions, and remains a subject ofinterest in its own right

Explore Bristol Research

Pinching of canards and folded nodes: nonsmooth approximation of slow-fast dynamics

https://research-information.bris.ac.uk/files/9636774/2012j_foldednode_.pdf

Pinching of canards and folded nodes: nonsmooth approximation of slow-fast dynamics

Abstract

Similar works

Full text

Available Versions

Explore Bristol Research