Title: Global analysis of a piecewise linear Lienard-type dynamical system

Authors: V.A. Gaiko, W.T. Van Horssen

Addresses: Department of Mathematics, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus. ' Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands

Abstract: In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary (but finite) number 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.

Keywords: piecewise dynamical systems; linear dynamical systems; field rotation parameter; bifurcation; limit cycle; planar dynamical systems; piecewise linear functions; dropping sections.

DOI: 10.1504/IJDSDE.2009.028038

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.1/2, pp.115 - 128

Published online: 02 Sep 2009 *

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