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Synchronization in repulsively coupled oscillators.

Simin Mirzaei1, Md Sayeed Anwar2, Fatemeh Parastesh1

  • 1Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 1591634311, Iran.

Physical Review. E
|February 17, 2023
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Summary
This summary is machine-generated.

Researchers developed a new method for achieving complete synchronization in repulsively coupled oscillators. This breakthrough enables identical oscillators to synchronize despite their repulsive coupling, a long-standing challenge in dynamical systems.

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Area of Science:

  • Dynamical Systems
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Coupled oscillators typically synchronize in phase or anti-phase.
  • Achieving complete synchronization in identical oscillators with purely repulsive coupling has been a significant challenge.

Purpose of the Study:

  • To introduce a general coupling condition for achieving complete synchronization in purely repulsively coupled oscillators.
  • To provide a method for designing coupling profiles that induce synchrony.

Main Methods:

  • Utilized the linear matrix of dynamical systems to define coupling conditions.
  • Employed the master stability function (MSF) approach for linear stability analysis.
  • Tested the proposed scheme on paradigmatic two-coupled chaotic oscillators.

Main Results:

  • Introduced a general coupling condition based on specific coupling matrices (profiles).
  • Demonstrated that these coupling profiles create a bidirectional cross-coupling link indicating synchronization onset.
  • Validated the effectiveness of the proposed condition for both two-oscillator and large ensemble systems.

Conclusions:

  • The proposed general coupling condition successfully enables complete synchronization in repulsively coupled identical oscillators.
  • The developed method is effective for diverse systems, including chaotic oscillators and large ensembles.
  • This work offers a novel approach to controlling synchronization in complex oscillatory networks.