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Using Hamiltonian control to desynchronize Kuramoto oscillators.

Oltiana Gjata1,2, Malbor Asllani2, Luigi Barletti1

  • 1Department of Mathematics & Computer Science, University of Florence, Viale Morgagni 67/A, 50134 Florence, Italy.

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Summary
This summary is machine-generated.

This study introduces a novel control method using Hamiltonian control theory to prevent detrimental synchronization in complex systems. The approach effectively impedes synchronization onset, enhancing system stability.

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Area of Science:

  • Complex Systems Dynamics
  • Control Theory
  • Network Science

Background:

  • Synchronization is a fundamental process in many natural and engineered systems, enabling collective behavior.
  • While often beneficial, synchronization can lead to instability, as seen in neurodegenerative diseases, epilepsy, and the Millennium Bridge incident.
  • Existing control methods may not adequately address the prevention of undesirable synchronization phenomena.

Purpose of the Study:

  • To develop and present an innovative control strategy to counteract and impede the onset of synchronization in complex systems.
  • To demonstrate the efficacy of Hamiltonian control theory in managing synchronization phenomena.
  • To investigate the application of this control method on a generalized Kuramoto model.

Main Methods:

  • Application of Hamiltonian control theory to introduce a small, stabilizing control term into the system dynamics.
  • Analysis of a generalized class of the paradigmatic Kuramoto model, a standard model for synchronization phenomena.
  • Mathematical formulation and simulation to assess the impact of the control term on synchronization onset.

Main Results:

  • The proposed control method successfully impedes the onset of synchronization in the studied systems.
  • The addition of a small control term effectively prevents the system from reaching a synchronized state.
  • The results demonstrate the robustness and applicability of the Hamiltonian control approach.

Conclusions:

  • Hamiltonian control theory offers a powerful and innovative method for preventing detrimental synchronization.
  • This approach can enhance the stability of complex systems prone to synchronization-induced instabilities.
  • The findings have potential implications for understanding and mitigating issues in fields ranging from neuroscience to structural engineering.