Slow divergence integral in regularized piecewise smooth systems
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...
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University of Szeged
2024-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10810 |
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| _version_ | 1850025394664636416 |
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| author | Renato Huzak Kristian Uldall Kristiansen Goran Radunovic |
| author_facet | Renato Huzak Kristian Uldall Kristiansen Goran Radunovic |
| author_sort | Renato Huzak |
| collection | DOAJ |
| description | 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 $VI_3$. 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. |
| format | Article |
| id | doaj-art-b9beeea55f2b404c8223d9468ff5d82d |
| institution | DOAJ |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-b9beeea55f2b404c8223d9468ff5d82d2025-08-20T03:00:51ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-03-0120241512010.14232/ejqtde.2024.1.1510810Slow divergence integral in regularized piecewise smooth systemsRenato Huzak0Kristian Uldall KristiansenGoran Radunovic1Hasselt University, Diepenbeek, BelgiumDepartment of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, DenmarkIn 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 $VI_3$. 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10810sliding limit cyclespiecewise smooth systemsregularization functionslow divergence integralminkowski dimension |
| spellingShingle | Renato Huzak Kristian Uldall Kristiansen Goran Radunovic Slow divergence integral in regularized piecewise smooth systems Electronic Journal of Qualitative Theory of Differential Equations sliding limit cycles piecewise smooth systems regularization function slow divergence integral minkowski dimension |
| title | Slow divergence integral in regularized piecewise smooth systems |
| title_full | Slow divergence integral in regularized piecewise smooth systems |
| title_fullStr | Slow divergence integral in regularized piecewise smooth systems |
| title_full_unstemmed | Slow divergence integral in regularized piecewise smooth systems |
| title_short | Slow divergence integral in regularized piecewise smooth systems |
| title_sort | slow divergence integral in regularized piecewise smooth systems |
| topic | sliding limit cycles piecewise smooth systems regularization function slow divergence integral minkowski dimension |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10810 |
| work_keys_str_mv | AT renatohuzak slowdivergenceintegralinregularizedpiecewisesmoothsystems AT kristianuldallkristiansen slowdivergenceintegralinregularizedpiecewisesmoothsystems AT goranradunovic slowdivergenceintegralinregularizedpiecewisesmoothsystems |