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Route to synchronization in coupled phase oscillators with frequency-dependent coupling: Explosive or continuous?

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  • 1Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.

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Summary

Transitions between incoherent and synchronized states in dynamical systems can be gradual or sudden. This study identifies key factors, frequency distribution and coupling strength correlations, that determine the nature of these synchronization transitions.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Interconnected dynamical systems exhibit transitions between incoherent and synchronized states.
  • These transitions can be continuous or explosive, with potential failure implications.
  • Understanding transition mechanisms is crucial for system stability.

Purpose of the Study:

  • Investigate mechanisms governing transitions between incoherent and synchronized dynamics.
  • Analyze routes to synchronization in globally coupled Kuramoto-like phase oscillators.
  • Determine factors influencing continuous versus explosive synchronization.

Main Methods:

  • Modeling dynamical networks as globally coupled Kuramoto-like phase oscillators.
  • Analyzing frequency-dependent coupling.
  • Quantifying oscillator natural frequency distribution using probability density function g(ω).
  • Defining frequency-coupling strength correlation function f(ω).

Main Results:

  • Identified conditions on f(ω) and g(ω) dictating continuous or explosive synchronization routes.
  • Explained the underlying physics governing these transitions.
  • Validated analytical findings with numerical simulations.

Conclusions:

  • The interplay between frequency distribution and coupling strength determines synchronization transition type.
  • Provides a framework for predicting and controlling system dynamics.
  • Offers insights into failure mechanisms in interconnected systems.