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Equations of Phase-Locked Loops: Dynamics on the Circle, Torus and Cylinder (World Scientific Series on Nonlinear Science Series a) (World Scientific Series on Nonlinear Science: Series a) [Hardcover]

By Jacek Kudrewicz (Author) & Stefan Wasowicz (Author)
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Item description for Equations of Phase-Locked Loops: Dynamics on the Circle, Torus and Cylinder (World Scientific Series on Nonlinear Science Series a) (World Scientific Series on Nonlinear Science: Series a) by Jacek Kudrewicz & Stefan Wasowicz...

Phase-Locked Loops (PLLs) are electronic systems that can be used as a synchronized oscillator, a driver or multiplier of frequency, a modulator or demodulator and as an amplifier of phase modulated signals. This book updates the methods used in the analysis of PLLs by drawing on the results obtained in the last 40 years. Many are published for the first time in book form. Nonlinear and deterministic mathematical models of continuous-time and discrete-time PLLs are considered and their basic properties are given in the form of theorems with rigorous proofs. The book exhibits very beautiful dynamics, and shows various physical phenomena observed in synchronized oscillators described by complete (not averaged) equations of PLLs. Specially selected mathematical tools are used the theory of differential equations on a torus, the phase-plane portraits on a cyclinder, a perturbation theory (Melnikov s theorem on heteroclinic trajectories), integral manifolds, iterations of one-dimensional maps of a circle and two-dimensional maps of a cylinder. Using these tools, the properties of PLLs, in particular the regions of synchronization are described. Emphasis is on bifurcations of various types of periodic and chaotic oscillations. Strange attractors in the dynamics of PLLs are considered, such as those discovered by Rssler, Henon, Lorenz, May, Chua and others.



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Item Specifications...


Studio: World Scientific Publishing Company
Pages   236
Est. Packaging Dimensions:   Length: 9.06" Width: 6.06" Height: 0.87"
Weight:   1.23 lbs.
Binding  Hardcover
Release Date   Aug 23, 2007
Publisher   World Scientific Publishing Company
ISBN  9812770909  
ISBN13  9789812770905  


Availability  0 units.


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Product Categories

1Books > Subjects > Computers & Internet > Computer Science > Circuitry > Circuit Components
2Books > Subjects > Professional & Technical > Engineering > Electrical & Electronics > Electricity Principles
3Books > Subjects > Professional & Technical > Engineering > Electrical & Optical > Circuits
4Books > Subjects > Professional & Technical > Engineering > Electrical & Optical > General
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Differential Equations
6Books > Subjects > Professional & Technical > Professional Science > Mathematics > Chaos & Systems
7Books > Subjects > Science > General
8Books > Subjects > Science > Mathematics > Applied > Differential Equations
9Books > Subjects > Science > Mathematics > Chaos & Systems



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