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Oscillation suppression in indirectly coupled limit cycle oscillators.

Neeraj Kumar Kamal1, Pooja Rani Sharma1, Manish Dev Shrimali1

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Summary

This study explores oscillation quenching in coupled oscillators. The environment's decay parameter critically influences amplitude death and oscillation death, with analytical and numerical results aligning.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Theoretical Physics

Background:

  • Oscillation quenching, including amplitude death (AD) and oscillation death (OD), is a key phenomenon in coupled oscillator systems.
  • Indirect coupling through a dynamic environment introduces complex emergent behaviors.
  • Understanding the role of environmental dynamics is crucial for controlling oscillator systems.

Purpose of the Study:

  • To investigate oscillation quenching in limit cycle oscillators coupled via a dynamic environment with exponential decay.
  • To analyze the influence of the environment's decay parameter and coupling strength on emergent dynamics.
  • To determine the critical conditions for oscillation quenching.

Main Methods:

  • Analytical investigation using linear stability analysis.
  • Numerical simulations to validate analytical findings.
  • Characterization of system dynamics as a function of coupling strength and decay parameter.

Main Results:

  • The decay parameter of the dynamic environment significantly impacts oscillation quenching phenomena (AD and OD).
  • Critical curves delineating regions of oscillation quenching were derived analytically.
  • Analytical predictions for quenching regions were found to be in excellent agreement with numerical simulations.

Conclusions:

  • The decay parameter of the environment is a critical factor in controlling oscillation quenching in indirectly coupled systems.
  • Linear stability analysis provides an accurate method for predicting oscillation quenching boundaries.
  • The findings offer insights into designing and controlling complex oscillatory networks.