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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Oscillations
  • Network Science

Background:

  • Tipping phenomena signify abrupt shifts in complex systems under parameter changes.
  • Coupled oscillators commonly exhibit continuous transitions with pairwise repulsive interactions.

Purpose of the Study:

  • To investigate the impact of higher-order repulsive interactions on the dynamics of coupled limit cycle oscillators.
  • To identify and characterize abrupt transitions to a 'death' state in such systems.
  • To explore the possibility of oscillation revival from the death state.

Main Methods:

  • Numerical simulations of coupled limit cycle oscillators.
  • Analysis of system dynamics under varying coupling strengths, including higher-order interactions.
  • Analytical determination of critical coupling strengths for tipping points.

Main Results:

  • Higher-order repulsive interactions induce an abrupt transition to a death state at lower coupling strengths than pairwise interactions.
  • A sudden revival of oscillations from the death state is observed with increased pairwise coupling.
  • The findings are robust for nonidentical oscillator systems.
  • Analytical predictions for critical coupling strengths closely match numerical simulations.

Conclusions:

  • Higher-order interactions fundamentally alter tipping dynamics in coupled oscillator systems.
  • The observed oscillation revival demonstrates complex emergent behavior and resilience.
  • The study provides a theoretical framework and validated predictions for abrupt transitions in complex systems.