Towards Theory of Piecewise Linear Dynamical Systems

2008/03/04 by Valery A. Gaiko, Wim T. van Horssen, Gaiko, Valery A. +1
Mathematics · Physics and Astronomy · #34C05 #34C07 #34C23 #37G10 #37G15 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0803.0490

openalex publication_date 2008/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system with k dropping sections and 2k+1 singular points can have at most k+2 limit cycles, k+1 of which surround the foci one by one and the last, (k+2)-th, limit cycle surrounds all of the singular points of this system.

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