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Oscillation death in diffusively coupled oscillators by local repulsive link.

C R Hens1, Olasunkanmi I Olusola, Pinaki Pal

  • 1CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 16, 2013
PubMed
Summary

Repulsive coupling can cause synchronized oscillators to cease oscillating, a phenomenon known as oscillation death. This effect was observed in coupled systems and networks, with the number of repulsive links remaining less than the network size.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Coupled oscillators are fundamental to many natural and engineered systems.
  • Synchronization phenomena in coupled oscillators are widely studied.
  • Emergent behaviors in complex networks can arise from local interactions.

Purpose of the Study:

  • To investigate the phenomenon of oscillation death in networks of coupled synchronized oscillators.
  • To analyze the role of repulsive coupling in inducing oscillation death.
  • To derive analytical conditions and confirm numerically the occurrence of oscillation death.

Main Methods:

  • Derivation of analytical conditions for oscillation death in coupled Landau-Stuart systems.
  • Numerical simulations of coupled Landau-Stuart systems.
  • Numerical simulations of chaotic systems, including Sprott and Rössler oscillators.
  • Analysis of large networks of globally coupled oscillators.

Main Results:

  • Oscillation death is reported in networks of coupled synchronized oscillators with repulsive coupling.
  • The number of repulsive links grows as the oscillation death scenario emerges.
  • Analytical conditions for oscillation death were derived for two coupled Landau-Stuart systems.
  • Numerical results confirmed oscillation death in both model and chaotic systems.
  • In large networks, the number of repulsive links was found to be less than the network size.

Conclusions:

  • Repulsive coupling is a viable mechanism for inducing oscillation death in synchronized oscillator networks.
  • The study provides both analytical and numerical evidence for oscillation death under repulsive coupling.
  • The findings are relevant to understanding emergent dynamics in complex coupled systems.