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We investigated generalized synchronization stability in coupled dynamical systems. Increasing the central node frequency in star networks enhances synchronization stability, while ring networks show less sensitivity to parameter changes.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Generalized synchronization is a key phenomenon in coupled dynamical systems.
  • Master stability function (MSF) is a powerful tool for analyzing synchronization stability.
  • Previous MSF applications were limited for degenerate eigenvalues in coupling matrices.

Purpose of the Study:

  • To extend the MSF approach for degenerate eigenvalues in coupling matrices.
  • To analyze the size instability in star and ring networks of coupled systems.
  • To investigate how network topology and parameters affect synchronization stability.

Main Methods:

  • Developed an extended Master Stability Function (MSF) approach.
  • Applied MSF to analyze size instability in star and ring network topologies.
  • Utilized coupled Rössler systems as a model for numerical verification.

Main Results:

  • Demonstrated that increasing the central node frequency in star networks enhances synchronization stability.
  • Showed that critical size for instability in star networks can be controlled by frequency.
  • Found that critical size in ring networks is largely unaffected by parameter variations.

Conclusions:

  • The extended MSF approach is effective for analyzing synchronization in complex networks.
  • Network parameters, specifically central node frequency in star networks, can be tuned to improve synchronization stability.
  • Ring network synchronization stability is robust against parameter variations.