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Synchronization of coupled Boolean phase oscillators.

David P Rosin1, Damien Rontani2, Daniel J Gauthier3

  • 1Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, Berlin D-10623, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

We developed Boolean phase oscillators with adjustable coupling strength using state-dependent feedback delay. This method enhances oscillator synchronization and is key for future large-scale coupled oscillator networks.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Coupled oscillators are fundamental to many natural and engineered systems.
  • Controlling coupling strength is crucial for understanding network dynamics.
  • Boolean oscillators offer a simplified yet powerful model for complex interactions.

Purpose of the Study:

  • To design and characterize Boolean phase oscillators with state-dependent feedback delay.
  • To investigate how adjustable coupling strength affects oscillator synchronization.
  • To explore the potential for large-scale networks of coupled oscillators.

Main Methods:

  • Designing Boolean phase oscillators with tunable feedback delay.
  • Experimentally and numerically coupling these oscillators in uni- and bidirectional configurations.
  • Analyzing locking ranges and Arnold tongues in parameter space.

Main Results:

  • State-dependent delay enables adjustable coupling strength with Boolean signals.
  • Increased coupling strength leads to larger locking ranges in both coupling schemes.
  • Unidirectional coupling reveals asymmetric Arnold tongues at frequency multiples.
  • Bidirectional coupling shows a symmetric locking region in frequency detuning and coupling strength parameter space.

Conclusions:

  • State-dependent feedback delay is an effective method for controlling coupling in Boolean oscillator networks.
  • The observed locking phenomena provide insights into network synchronization dynamics.
  • This work lays the foundation for scalable experimental networks to study complex system dynamics.