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Increasing network size enhances synchronizability in coupled systems with connection delays. Larger networks mitigate the negative impact of delays, promoting synchronization unlike smaller networks.

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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Systems Engineering

Background:

  • Network synchronizability is crucial for many natural and engineered systems.
  • Connection delays can impede or destabilize synchronization in coupled networks.
  • Understanding network-scale effects is essential for designing robust synchronized systems.

Purpose of the Study:

  • To investigate the impact of network scale on the synchronizability of fully coupled networks with connection delays.
  • To analyze how increasing network size affects the stability of synchronization in the presence of time delays.

Main Methods:

  • Derivation of the master stability function by separating synchronization and transverse directions.
  • Introduction of a novel time variable within the master stability function.
  • Analysis of two specific networks composed of typical nonlinear dynamical systems.

Main Results:

  • The master stability function reveals that increasing network scale weakens the detrimental effect of connection delays.
  • Synchronization stability is enhanced in larger networks compared to smaller ones when connection delays are present.
  • Empirical validation through case studies on specific network configurations.

Conclusions:

  • Network scale is a critical factor in overcoming the destabilizing effects of connection delays on synchronization.
  • Larger networks exhibit improved synchronizability, making them more robust to time delays.
  • Findings offer insights for designing large-scale synchronized systems in various scientific and engineering domains.