Contribution to Book
Discrete phase-locked loop systems and spreadsheetsModels and Applications of Chaos Theory in Modern Science
Date of this Version1-1-2011
Document TypeBook Chapter
AbstractThis 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 InformationSergei 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/