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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Optimizing disorder with machine learning to harness phase synchronization.

Jun-Yin Huang1, Zheng-Meng Zhai1, Li-Li Ye1

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Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

Disorder can surprisingly enhance synchronization in complex systems. Machine learning frameworks can now design optimal disorder configurations to maximize this effect, offering efficient optimization for dynamical networks.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Machine learning

Background:

  • Disorder is typically viewed as detrimental to system coherence.
  • However, specific conditions can enable disorder to promote synchronization.
  • Understanding and controlling disorder-induced synchronization is crucial for complex dynamical networks.

Purpose of the Study:

  • To develop a machine-learning framework for the inverse design of optimal-disorder configurations.
  • To maximize phase synchronization in coupled driven nonlinear systems.
  • To efficiently explore high-dimensional parameter spaces for synchronization optimization.

Main Methods:

  • Utilized an array of forced and damped nonlinear pendulums with controlled disorder and noise.
  • Trained a feedforward neural network (FNN) to predict synchronization strength (Shannon entropy index) from disorder parameters.
  • Employed the FNN as a surrogate for computationally intensive stochastic differential equation simulations.

Main Results:

  • The trained FNN accurately predicted synchronization strength based on disorder parameters.
  • The framework efficiently identified optimal disorder configurations that maximize phase synchronization.
  • Demonstrated that machine learning can capture and optimize disorder-induced synchronization.

Conclusions:

  • Machine learning provides an effective tool for optimizing synchronization in complex dynamical networks.
  • Inverse design using ML can identify beneficial roles of disorder in system coherence.
  • This approach offers a computationally efficient alternative to traditional simulation methods.