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Limit Cycle Bifurcations of a Piecewise Linear Dynamical System

Valery A. Gaiko
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number of dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we give a sketch of the proof of the theorem stating 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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