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Online ISSN 1552-4485; Print ISSN 0033-569X
Nonlinear oscillations in a distributed network
Author:
Robert K. Brayton
Journal:
Quart. Appl. Math. 24 (1967), 289-301
DOI:
https://doi.org/10.1090/qam/99914
MathSciNet review:
QAM99914
Full-text PDF Free Access
Abstract | References | Additional Information
Abstract: The oscillations of small amplitude in a lossless transmission line terminated with a nonlinear circuit are studied by perturbation theory. The equations describing this system are reduced to a difference-differential equation with one delay. A general procedure is given for equations of this type for finding the expansion of the oscillation to any order in terms of the coefficient of the fundamental frequency. The frequency-amplitude relations are obtained to second order and compared with results found on the computer. Both the autonomous and forced cases are studied. It is indicated in the forced case that the frequency-amplitude relation gives approximately the range of “locking in".
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Additional Information
Article copyright:
© Copyright 1967
American Mathematical Society