NDLI: The piecewise-linear Lorenz circuit is chaotic in the sense of Shilnikov

Content Provider	IEEE Xplore Digital Library
Author	Tokunaga, R. Matsumoto, T. Chua, L.O. Miyama, S.
Copyright Year	1974
Abstract	The authors prove that the piecewise-linear Lorenz circuit is chaotic in the sense of Shilnikov. They first prove the existence of a heteroclinic orbit, and then prove an inequality among the eigenvalues. In addition to a detailed analysis of the piecewise linear dynamics, interval analysis is utilized to prove various inequalities. This novel approach can be applied to many other problems that require proving rigorously the existence of either a homoclinic or a heteroclinic orbit. With this proof, the piecewise-linear Lorenz circuit becomes one of the very few real physical systems where chaos has been observed by laboratory measurement, confirmed by simulation, and proved mathematically.<>
Starting Page	766
Ending Page	786
Page Count	21
File Size	1352066
File Format	PDF
ISSN	00984094
Volume Number	37
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1990-06-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Piecewise linear techniques Chaos Voltage Eigenvalues and eigenfunctions Differential equations Jacobian matrices Circuits and systems Laboratories Extraterrestrial measurements Circuit simulation
Content Type	Text
Resource Type	Article
Subject	Engineering

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