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Controlling cluster synchronization by adapting the topology.

Judith Lehnert1, Philipp Hövel2, Anton Selivanov3

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.

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

This study introduces an adaptive control scheme for synchronizing delay-coupled networks. The method dynamically adjusts network topology to achieve desired synchronization states, robustly controlling complex systems.

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Area of Science:

  • Complex Systems and Network Science
  • Nonlinear Dynamics and Control Theory

Background:

  • Synchronization phenomena are crucial in various natural and engineered systems.
  • Controlling synchronization in networks with time delays presents significant challenges.

Purpose of the Study:

  • To develop an adaptive control scheme for achieving in-phase and cluster synchronization in delay-coupled networks.
  • To ensure the control scheme is robust against varying initial conditions and coupling parameters.

Main Methods:

  • Utilized the speed-gradient method to adapt network topology dynamically.
  • Investigated the role of excitatory and inhibitory links in stabilizing cluster states.
  • Analyzed the impact of delay time as a critical parameter.

Main Results:

  • Successfully demonstrated robust control of synchronization in delay-coupled networks.
  • Identified a specific interplay of link types and delay time for stabilizing desired cluster states.
  • Showcased the ability to construct networks exhibiting specific cluster states and oscillation frequencies.

Conclusions:

  • The proposed adaptive control scheme effectively manages synchronization in complex networks.
  • The method's robustness and applicability to generic models like the Stuart-Landau oscillators suggest broad potential.
  • Potential applications span physics, chemistry, technology, and life sciences, highlighting the universality of the findings.