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Tipping in Stuart-Landau oscillators induced by higher-order repulsive interactions
Umesh Kumar Verma1,2, Subhasanket Dutta1, Richita Ghosh2
1Complex Systems Lab, Department of Physics, <a href="https://ror.org/01hhf7w52">Indian Institute of Technology Indore</a>, Khandwa Road, Simrol, Indore-453 552, India.
Physical Review. E
|November 20, 2024
Summary
Complex systems exhibit tipping points, leading to abrupt state changes. This study reveals a novel transition from oscillation to death in coupled oscillators due to higher-order interactions, with potential for oscillation revival.
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.
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