Solitary death in coupled limit cycle oscillators with higher-order interactions
Subhasanket Dutta1, Umesh Kumar Verma1, Sarika Jalan1
1Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India.
Physical Review. E
|January 20, 2024
Summary
This study introduces higher-order interactions in coupled oscillators, revealing an explosive transition to a solitary death state via homoclinic bifurcation. This finding has implications for understanding complex dynamics, including those in epileptic seizures.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Theoretical physics
Background:
- Coupled limit cycle oscillators commonly exhibit phase transitions to amplitude or oscillation death.
- Existing models primarily focus on pairwise interactions.
Purpose of the Study:
- To investigate the effects of higher-order interactions, not reducible to pairwise couplings, on oscillator dynamics.
- To explore novel phase transitions and emergent states in coupled Stuart-Landau oscillators.
Main Methods:
- Incorporation of higher-order interaction schemes into coupled Stuart-Landau oscillator models.
- Analysis of dynamical evolution and phase transitions using numerical simulations.
- Analytical determination of critical coupling strengths.
Main Results:
- Discovery of a solitary death state achieved through a first-order, explosive phase transition.
- Identification of homoclinic bifurcation as the mechanism driving the explosive death state.
- Observation of amplitude surge and oscillation revival preceding and following the transition.
Conclusions:
- Higher-order interactions can lead to unique dynamical states, such as the solitary death state.
- The identified explosive transition mechanism differs from typical subcritical Hopf bifurcations.
- The findings offer insights into complex dynamics, with potential parallels to epileptic seizure dynamics.
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