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http://hdl.handle.net/1942/38785
Title: | The number of limit cycles for regularized piecewise polynomial systems is unbounded | Authors: | HUZAK, Renato Uldall Kristiansen, Kristian |
Issue Date: | 2022 | Publisher: | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 342 , p. 34 -62 | Abstract: | In this paper, we extend the slow divergence-integral from slow-fast systems, due to De Maesschalck, Dumortier and Roussarie, to smooth systems that limit onto piecewise smooth ones. In slow-fast systems, the slow divergence-integral is an integral of the divergence along a canard cycle with respect to the slow time and it has proven very useful in obtaining good lower and upper bounds of limit cycles in planar polynomial systems. In this paper, our slow divergence-integral is based upon integration along a generalized canard cycle for a piecewise smooth two-fold bifurcation (of type visible-invisible). We use this framework to show that the number of limit cycles in regularized piecewise smooth polynomial systems is unbounded. | Keywords: | Slow divergence-integral;Canards;Piecewise smooth systems;Two-folds;GSPT | Document URI: | http://hdl.handle.net/1942/38785 | Link to publication/dataset: | https://www.sciencedirect.com/science/article/pii/S0022039622005605 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2022.09.028 | ISI #: | 000914679600003 | Rights: | 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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