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Periodic external driving of transmission-delay-coupled phase oscillator system: Switching between different twisted
Jin-Song Kang1, Yong-Hyok An1, Ryong-Son Kim1
1Research Group for Nonlinear Dynamics, Department of Physics, University of Science, Unjong-District, Pyongyang, Democratic People's Republic of Korea.
Chaos (Woodbury, N.Y.)
|December 3, 2024
Summary
External periodic forcing on coupled phase oscillators can lead to two entrainment regimes: forced and drifting. Drifting entrainment can induce novel twisted states with unique phase gradients and traveling order parameter amplitudes.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Theoretical physics
Background:
- Spatially extended systems of coupled oscillators are fundamental in various scientific fields.
- Understanding the impact of external periodic forcing and transmission delays is crucial for predicting system behavior.
- Phase oscillator models are widely used to study synchronization phenomena.
Purpose of the Study:
- To investigate the effects of external periodic forcing on phase oscillators with transmission delays.
- To analyze the stability diagram and identify different entrainment regimes.
- To characterize novel states, such as twisted states, induced by the forcing.
Main Methods:
- Analysis of the continuum limit (N→∞) of the model system.
- Utilizing the Ott-Antonsen invariant manifold for stability analysis.
- Deriving the stability boundary for forced entrainment.
- Direct numerical simulations to validate theoretical findings.
Main Results:
- Identified two entrainment regimes: forced and drifting.
- Determined the stability boundary for the forced entrainment regime.
- Discovered that drifting entrainment can trigger unusual twisted states.
- Showcased the ability to switch between twisted states by adjusting forcing strength.
Conclusions:
- External periodic forcing significantly influences the dynamics of coupled phase oscillators with delays.
- Drifting entrainment offers a pathway to novel complex states (twisted states).
- The study provides a comprehensive stability diagram and insights into controlling oscillator behavior.
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