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Stochastic master stability function for noisy complex networks.

Fabio Della Rossa1, Pietro DeLellis2

  • 1Department of Electronics, Information, and Bioengineering, 20133 Politecnico of Milan, Italy and Department of Electrical Engineering and Information Technology, University of Naples, 80125 Federico II, Italy.

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Noise can aid synchronization in complex networks when evenly distributed. However, unevenly distributed or excessive noise can disrupt network synchronizability, impacting system stability.

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Area of Science:

  • Complex networks
  • Stochastic dynamical systems
  • Synchronization theory

Background:

  • Understanding synchronization in complex networks is crucial for various fields.
  • The impact of noise on network dynamics, particularly synchronization, remains a key research question.

Purpose of the Study:

  • To extend the master stability function approach for analyzing synchronization in complex networks of stochastic systems.
  • To derive conditions for exponential stability and quantify the effects of noise on synchronizability.

Main Methods:

  • Broadened the master stability function approach.
  • Developed necessary and sufficient conditions for exponential stability.
  • Conducted extensive simulations on paradigmatic networks of noisy systems.

Main Results:

  • Identified conditions under which noise enhances synchronization (even diffusion).
  • Demonstrated that excessive or localized noise can impair network synchronizability.
  • Quantified the differential impact of noise on network stability.

Conclusions:

  • Noise's effect on synchronization is highly dependent on its distribution within the network.
  • The master stability function approach provides a robust framework for analyzing noise-induced synchronization phenomena.
  • Findings offer insights into designing more robust and synchronizable complex systems.