On a Hysteresis Oscillator Including Periodic Thresholds

Ken'ichi KOHARI  Toshimichi SAITO  Hiroshi KAWAKAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.12   pp.2102-2107
Publication Date: 1993/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Circuits and Systems
relaxation oscillator,  synchronization,  hysteresis,  piecewise-linear system,  torus,  

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In this article, we consider a hysteresis oscillator which includes periodic thresholds. This oscillator relates to a model of human's sleep-wake cycles. Deriving a one dimensional return map rigorously, we can clarify existence regions of various periodic attractors in some parameter subspace. Also, we clarify co-existence regions of periodic attractors and existence regions of quasi-periodic attractors. Some of theoretical results are confirmed by laboratory measurements.