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Continuous and discontinuous transitions to synchronization.

Chaoqing Wang1, Nicolas B Garnier2

  • 1Department of Physics, East China Normal University, Shanghai 200062, China.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

The transition to synchronization in Stuart-Landau oscillators shifts from continuous to discontinuous with reactive coupling. This occurs due to co-existing synchronized and incoherent states, unlike the Kuramoto model.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Statistical physics

Background:

  • Synchronization is a fundamental phenomenon in coupled oscillator systems.
  • The Kuramoto model is a standard paradigm for studying synchronization transitions.
  • Understanding transitions in coupled oscillator systems is crucial for various scientific fields.

Purpose of the Study:

  • To investigate the impact of coupling type (diffusive vs. reactive) on synchronization transitions in Stuart-Landau oscillators.
  • To explain the mechanism behind the shift from continuous to discontinuous synchronization.
  • To compare the observed behavior with the established Kuramoto model.

Main Methods:

  • Analysis of a system of globally coupled Stuart-Landau oscillators.
  • Mathematical modeling to describe the dynamics of synchronization.
  • Investigation of parameter ranges where different macrostates coexist.

Main Results:

  • A transition from continuous to discontinuous synchronization is observed when coupling changes from diffusive to reactive.
  • This discontinuous transition arises from the coexistence of synchronized and incoherent macrostates.
  • The synchronized state at the transition involves a finite number of oscillators, differing from the Kuramoto model.

Conclusions:

  • Reactive coupling can induce discontinuous synchronization transitions in Stuart-Landau oscillator systems.
  • The coexistence of stable incoherent and synchronized macrostates is key to this phenomenon.
  • The findings offer insights into discontinuous transitions and their mechanisms in complex systems.