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Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling.

S Chakraborty1, M Dandapathak2, B C Sarkar3

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This study analyzes oscillation quenching in coupled third-order phase-locked loops (PLLs). We identified conditions for amplitude death and inhomogeneous steady states, crucial for understanding coupled oscillator dynamics.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Electrical Engineering

Background:

  • Coupled oscillators exhibit complex behaviors like amplitude death and inhomogeneous steady states.
  • Phase-locked loops (PLLs) are fundamental in signal processing and communication systems.
  • Understanding oscillation quenching in coupled PLLs is vital for system stability and performance.

Purpose of the Study:

  • To analytically investigate oscillation quenching phenomena in coupled third-order PLLs.
  • To determine the parameter space regions for amplitude death and inhomogeneous steady states.
  • To examine the influence of system parameters and coupling on quenched states.

Main Methods:

  • Analytical exploration of oscillation quenching.
  • Application of Routh-Hurwitz stability criterion to identify quenched state limits.
  • Numerical simulations to validate analytical findings.
  • Investigation of both periodic and chaotic modes of operation.

Main Results:

  • Identified lower and upper parameter limits for quenched states using Routh-Hurwitz technique.
  • Demonstrated that convergence to quenched states depends on design parameters.
  • Observed homogeneous steady states for identical systems and inhomogeneous steady states for non-identical systems.
  • Found wider quenched states for identical systems compared to non-identical ones.
  • Noted narrowing of quenched states when individual loops operate in chaotic mode.

Conclusions:

  • The study provides a comprehensive analytical and numerical understanding of oscillation quenching in coupled third-order PLLs.
  • Parameter tuning is critical for achieving desired quenched states (amplitude death or inhomogeneous steady states).
  • System parameter differences and chaotic dynamics significantly influence the stability and extent of quenched states.