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Enhancing Synchronization by Optimal Correlated Noise

Jong-Min Park

at NEST meeting (KIAS), 1 Apr. 2022

[PRL 128, 098301 (2022)]

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Motivation

The synchronization of coupled oscillators is widely study phenomena.

Noise is unavoidable, thus has to be concerned.

Is noise beneficial or disadvantageous for synchronization?

 

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Outline

We study the optimal noise in the Kuramoto model.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Optimal noise is analyzed in …

    • Simplest two-body system
    • Many-body system in periodic chains
    • Many-body system in complex networks

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Two oscillators – relative coordinate

 

 

Order parameter depends only on the relative angle,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Two oscillators – effective noise

relevant parameter is the effective noise strength

 

 

 

specific cases

 

 

 

    • common noise

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    • uncorrelated noise

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    • anti-correlated noise

 

 

 

 

 

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Two oscillators – noise effect in synchronization

Numerical result shows that generally

 

 

 

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Two oscillators – optimal correlation

 

 

 

 

 

 

 

 

 

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Two oscillators – optimal correlation

 

 

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Optimization for general cases – centered dynamics

 

 

The equation and the order parameter are translation-invariant.

 

 

For example,

 

 

 

 

 

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Optimization for general cases – linearized equation

 

 

 

 

 

 

In the form of matrix representation, it is written as

 

 

 

}

 

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Optimization for general cases – objective function

 

 

 

The expansion of the order parameter is

 

 

 

 

 

 

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Oscillators in periodic chains – optimal noise

 

The optimal is more effective than the uncorrelated noise.

 

 

 

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Oscillators in periodic chains – transition of patterns

Near the critical point, the optimal noise exhibit a transition form local to global structure.

 

 

 

 

 

 

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Oscillators in complex network

In a complex network, the checker-board pattern forms clusters.

IEEE 14-node

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Oscillators in complex network

In a complex network, the checker-board pattern forms clusters.

IEEE 30-node

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Summary

  • In the sub-critical region, the noise enhances the synchronization.
  • There is optimal noise correlations,�and they exhibit a transition between anti-correlated and correlated noises.
  • In a complex network, the optimal noise is generally anti-correlated.
  • Depending on network, the optimal noise correlation shows diverse patterns:�for example, decaying or clustering.