Rich Superstable Phenomena in a Piecewise Constant Nonautonomous Circuit with Impulsive Switching

Yusuke MATSUOKA  Toshimichi SAITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2767-2774
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2767
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Oscillation, Dynamics and Chaos
chaos,  bifurcation,  piecewise constant systems,  superstable periodic orbits,  

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This paper studies rich superstable phenomena in a nonautonomous piecewise constant circuit including one impulsive switch. Since the vector field of circuit equation is piecewise constant, embedded return map is piecewise linear and can be described explicitly in principle. As parameters vary the map can have infinite extrema with one flat segment. Such maps can cause complicated periodic orbits that are superstable for initial state and are sensitive for parameters. Using a simple test circuit typical phenomena are verified experimentally.