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Analysis of Border-Collision Bifurcations in a Flow Model of a Switching System
Hiroto TANAKA Toshimitsu USHIO
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2002/04/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section of Selected Papers from the 14th Workshop on Circuits and Systems in Karuizawa)
flow model, piecewise linear system, switching system, border-collision bifurcation,
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In this paper, we consider a switching system modeled by a discrete-time flow model. By simulation, it is shown that a lot of border-collision bifurcations occur since the system is piecewise linear. By using its characteristics, we classify its dynamics into modes, and we define blocks and a kind of Poincare map based on the modes. We calculate occurrence conditions of each block and all the Poincare points by computer-assisted analysis. We consider two bifurcation phenomena, and we show that a Poincare point hits a boundary of the occurrence conditions of a block. So, both bifurcations are indeed border-collision bifurcations.