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Title: | Slow divergence integral in regularized piecewise smooth systems | Authors: | HUZAK, Renato Kristiansen, Kristian Uldall Radunovic, Goran |
Issue Date: | 2024 | Publisher: | UNIV SZEGED, BOLYAI INSTITUTE | Source: | Electronic Journal of Qualitative Theory of Differential Equations, 15 , p. 1 -20 | Abstract: | In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence integral is invariant under smooth equivalences. This is a natural generalization of the notion of slow divergence integral along normally hyperbolic portions of curve of singularities in smooth planar slow–fast systems. We give an interesting application of the integral in a model with visible-invisible two-fold of type VI3. It is related to a connection between so-called Minkowski dimension of bounded and monotone “entry-exit” sequences and the number of sliding limit cycles produced by so-called canard cycles. | Keywords: | sliding limit cycles;piecewise smooth systems;regularization function;slow divergence integral;Minkowski dimension. | Document URI: | http://hdl.handle.net/1942/42753 | Link to publication/dataset: | https://www.math.u-szeged.hu/ejqtde/p10810.pdf | ISSN: | 1417-3875 | e-ISSN: | 1417-3875 | DOI: | 10.14232/ejqtde.2024.1.15 | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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p10810.pdf Restricted Access | Published version | 867.9 kB | Adobe PDF | View/Open Request a copy |
PaperEJQTDE.pdf Until 2024-10-01 | 777.18 kB | Adobe PDF | View/Open Request a copy |
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