Controlling Canard Cycles
Keyword(s):
Blow Up
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AbstractCanard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed ordinary differential equations). It is well known that canard cycles are difficult to detect, hard to reproduce numerically, and that they are sensible to exponentially small changes in parameters. In this paper, we combine techniques from geometric singular perturbation theory, the blow-up method, and control theory, to design controllers that stabilize canard cycles of planar fast-slow systems with a folded critical manifold. As an application, we propose a controller that produces stable mixed-mode oscillations in the van der Pol oscillator.
2020 ◽
Vol 406
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pp. 132493
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2017 ◽
Vol E100.A
(7)
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pp. 1522-1531
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2014 ◽
Vol 34
(1)
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pp. 81-92
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2021 ◽
Vol 31
(08)
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pp. 2150121
2015 ◽
Vol 25
(2)
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pp. 023105
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1998 ◽
Vol 08
(03)
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pp. 505-519
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2021 ◽
Vol 31
(7)
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pp. 073133
2012 ◽
Vol 241
(18)
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pp. 1518-1526
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