Sliding cycles of the regularized piecewise linear VI₃ two-fold

2023/10/11 by Renato Huzak, Huzak, Renato, Kristian Uldall Kristiansen +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Microtubule and mitosis dynamics

paper · pdf · doi:10.48550/arxiv.2310.07230

openalex publication_date 2023/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to study the number of sliding limit cycles of a regularized piecewise linear VI₃ two-fold using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the half-plane with an invisible fold point. We prove that the integral has at most 1 zero counting multiplicity (when it is not identically zero). This will imply that the canard cycles can produce at most 2 limit cycles. Moreover, we detect regions in the parameter space with 2 limit cycles.

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