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Explosive death induced by mean-field diffusion in identical oscillators.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Statistical physics

Background:

  • Coupled oscillators exhibit diverse collective behaviors.
  • Mean-field diffusion is a common coupling mechanism.
  • Oscillator death signifies a loss of collective oscillations.

Purpose of the Study:

  • To report the first observation of an explosive death transition in coupled oscillators.
  • To investigate this transition in both limit cycle and chaotic systems.
  • To determine the general conditions and characteristics of this phenomenon.

Main Methods:

  • Simulations of ensembles of identical limit cycle and chaotic oscillators.
  • Coupling via mean-field diffusion.
  • Analysis of normalized amplitude variation with coupling strength.
  • Linear stability analysis to determine transition points.

Main Results:

  • An abrupt and irreversible transition to a death state was observed from an oscillatory state.
  • This first-order phase transition was independent of system size.
  • The transition was found in systems with co-existing in-phase oscillations and a coupling-dependent homogeneous steady state.
  • Calculated backward transition points using linear stability analysis agreed with numerical results.

Conclusions:

  • An explosive death transition is a general phenomenon in coupled oscillator systems under specific conditions.
  • The transition is a first-order phase transition, robust to system size.
  • Linear stability analysis accurately predicts the transition dynamics.