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• W2279228514 abstract "The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of the local dynamics, namely trajectories that flow from attractive regions of space into repulsive regions. An alternative way to model switches between timescales is using piecewise-smooth differential equations. There is presently no adequate theory or method for relating slow-fast and piecewise-smooth models. Here we derive the analogous piecewise-smooth system for the folded node by pinching phase space to sharpen the switch between timescales. The corresponding piecewise-smooth system contains a so-called two-fold singularity, and exhibits the same topology and number of canards as the slow-fast system. Thus pinching provides a piecewise-smooth approximation to a slow-fast system." @default.
• W2279228514 created "2016-06-24" @default.
• W2279228514 creator A5077245992 @default.
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• W2279228514 date "2015-06-02" @default.
• W2279228514 modified "2023-09-27" @default.
• W2279228514 title "Nonsmooth analogues of slow-fast dynamics -- pinching at a folded node" @default.
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