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Contribution to Book
Discrete phase-locked loop systems and spreadsheets
Models and Applications of Chaos Theory in Modern Science
  • Sergei Abramovich, State University of New York
  • Elena Kudryashova, Saint Petersburg State University
  • Gennady A. Leonov, Saint Petersburg State University
  • Stephen Sugden, Bond University
Date of this Version
1-1-2011
Document Type
Book Chapter
Publication Details

Citation only.

Abramovich, S., Kudryashova, E., Leonov, G. A., & Sugden, S. (2011). Discrete phase-locked loop systems and spreadsheets. In E. Zeraooulia (Ed.), Models and Applications of Chaos Theory in Modern Science (pp. 405-428). United States: Science Publishers.

Access the publisher's website.

2011 HERDC submission. FoR code: 130208

© Copyright CRC Press, 2011

ISBN
978-1-57808-722-8
Disciplines
Abstract
This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behavior interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behavior of systems with different types of non-linear characteristic.
Citation Information
Sergei Abramovich, Elena Kudryashova, Gennady A. Leonov and Stephen Sugden. "Discrete phase-locked loop systems and spreadsheets" 1stUnited StatesModels and Applications of Chaos Theory in Modern Science (2011) p. 405 - 428
Available at: http://works.bepress.com/sergei_abramovich/12/