Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canard-like phenomena in piecewise-smooth Van der Pol systems   We show that a nonlinear, piecewise-smooth, planar dynamical system can
exhibit canard phenomena. Canard solutions and explosion 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.

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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph