Analysis of Border-Collision Bifurcations in a Flow Model of a Switching System

Hiroto TANAKA  Toshimitsu USHIO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.4   pp.734-739
Publication Date: 2002/04/01
Online ISSN: 
DOI: 
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)
Category: 
Keyword: 
flow model,  piecewise linear system,  switching system,  border-collision bifurcation,  

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Summary: 
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.