Slow divergence integral in regularized piecewise smooth systems

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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Bibliographic Details
Main Authors: Renato Huzak, Kristian Uldall Kristiansen, Goran Radunovic
Format: Article
Language:English
Published: University of Szeged 2024-03-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Subjects:
sliding limit cycles
piecewise smooth systems
regularization function
slow divergence integral
minkowski dimension
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=10810
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Summary: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.
ISSN:1417-3875

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