Discrete Phase-Locked Loop Systems and Spreadsheets

Discrete Phase-Locked Loop Systems and Spreadsheets

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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 Epidemiological Survey of the Main Tick-Borne Pathogens Infecting Dogs from the Republic of Moldova 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 Leasing as an instrument for innovative development of agricultural enterprises 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.