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Synchronization and beam forming in an array of repulsively coupled oscillators
N F Rulkov1, L Tsimring, M L Larsen
1Institute for Nonlinear Science, University of California-San Diego, La Jolla, CA 92093-0402, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
We investigated coupled Stuart-Landau oscillators. Repulsive coupling leads to synchronized states, and external driving can synchronize the array for applications in phase array antennas.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Array signal processing
Background:
- Coupled oscillator systems exhibit complex dynamics.
- Stuart-Landau oscillators are a fundamental model for studying synchronization phenomena.
- Phase array antennas require precise control over signal phases.
Purpose of the Study:
- To analyze the synchronization dynamics of an array of Stuart-Landau oscillators with repulsive coupling.
- To investigate the effect of external driving on the oscillator array's mean field and phase locking.
- To explore the application of this synchronized oscillator array in phase array antenna beamforming.
Main Methods:
- Numerical simulations of coupled Stuart-Landau oscillators.
- Analysis of network synchronization regimes and mean field dynamics.
- Investigation of phase locking phenomena under external oscillatory forcing.
Main Results:
- Autonomous arrays with repulsive coupling achieve synchronized states with a zero mean field.
- External driving induces a nonzero mean field that tracks the driving signal.
- Sufficiently strong external driving synchronizes the oscillators and locks their phases.
Conclusions:
- Repulsive coupling in Stuart-Landau oscillator arrays leads to diverse synchronized states.
- External driving offers a mechanism to control and synchronize oscillator arrays.
- Synchronized oscillator arrays show potential for enhancing phase array antenna performance by reshaping signal phases.
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