Slow divergence integral in regularized piecewise smooth systems

Author:

Huzak Renato1ORCID,Kristiansen Kristian Uldall2ORCID,Radunovic Goran3ORCID

Affiliation:

1. Hasselt University

2. Technical University of Denmark

3. University of Zagreb

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 V I 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.

Publisher

University of Szeged

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds;Qualitative Theory of Dynamical Systems;2024-08-16

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