Global analysis of a piecewise linear Lienard-type dynamical system
by V.A. Gaiko, W.T. Van Horssen
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 2, No. 1/2, 2009

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.

Online publication date: Wed, 02-Sep-2009

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