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Related Experiment Videos

Extreme sensitivity to detuning for globally coupled phase oscillators.

Peter Ashwin1, Oleksandr Burylko, Yuri Maistrenko

  • 1Department of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, United Kingdom.

Physical Review Letters
|February 21, 2006
PubMed
Summary

Coupled oscillators exhibit extreme sensitivity to frequency detuning with three or more units. This sensitivity, where frequency locking is easily disrupted, emerges robustly in populations of five or more coupled oscillators.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Populations of coupled oscillators are fundamental to understanding synchronization phenomena in diverse systems.
  • The natural frequencies of individual oscillators (detuning) can significantly impact collective behavior and stability.
  • Investigating sensitivity to detuning is crucial for predicting system robustness and emergent properties.

Purpose of the Study:

  • To analyze the sensitivity of globally coupled phase oscillators to variations in their natural frequencies (detuning).
  • To identify the conditions under which populations of coupled oscillators exhibit extreme sensitivity to detuning.
  • To determine how the number of oscillators (N) influences the emergence and robustness of this extreme sensitivity.

Main Methods:

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  • Mathematical analysis of N globally coupled phase oscillators.
  • Investigation of bifurcations leading to states of extreme sensitivity.
  • Systematic examination of sensitivity across different population sizes (N=2, 3, 4, and N>=5).

Main Results:

  • Extreme sensitivity, where frequency locking is destroyed by arbitrarily small detuning, is absent for N=2 oscillators.
  • For N=3 and N=4, extreme sensitivity appears only at isolated parameter values.
  • Robust emergence of extreme sensitivity is observed for open sets of parameter values when N>=5.

Conclusions:

  • The number of coupled oscillators critically determines the system's sensitivity to frequency detuning.
  • Populations of five or more globally coupled phase oscillators can robustly exhibit extreme sensitivity to detuning.
  • Understanding these detuning effects is vital for designing and predicting the behavior of synchronized systems.