Coupled Phase-Locked Loops

Coupled Phase-Locked Loops

Stability, Synchronization, Chaos and Communication with Chaos

Valery V Matrosov, Vladimir D Shalfeev


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Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and ensembles, formed by interacting dynamical elements.

Unfortunately, the applicability of analytical and qualitative methods of nonlinear dynamics to such complex systems is severely restricted due to the high dimension of phase space. Therefore, studying the simplest models of networks, which are ensembles with a small number of elements, becomes of particular interest. Such models allow to make use of the entire spectrum of analytical, qualitative, and numerical methods of nonlinear dynamics. This book is devoted to the investigation of a kind of such systems, namely small ensembles of coupled, phase-controlled oscillators. Both traditional issues, like synchronization, that are relevant for applications in radio-communications, radio-location, energy, etc., and nontraditional issues of excitation of chaotic oscillations and their possible application in advanced communication systems are addressed.

  • Introduction: Dynamical Chaos and Information Communication
  • Nonlinear Dynamics of the Phase System
  • Cascade Coupling of Two Phase Systems
  • Three Cascade-Coupled Phase System Dynamics
  • Phase Systems Parallel Coupling
  • Synchronization of Chaotic Oscillations
  • Communication with Chaos
  • Conclusion

Readership: Graduate students and researchers in physics, biology and applied mathematics interested in nonlinear dynamics, as well as radioengineers.
Phase Locked Loop (PLL);Ensemble of Coupled PLLs;Collective Dynamics of Ensemble;Synchronization;Chaos;Bifurcations;Communication with Chaos0Key Features:
  • Presents new original results of theoretical study and computer simulation of collective dynamics phenomena of small ensembles of coupled phase locked loops (PLL)
  • Original detailed research of the various chaos modes of coupled PLLs serves as an effective source of chaotically modulated oscillations, with central frequency stabilized by reference frequency with applications
  • Written by prominent experts in nonlinear dynamics with vast experience as lecturers and researchers in universities worldwide