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Stable synchronization in networks of identical coupled oscillators is possible even with asymmetric connections. This study mathematically proves previous findings incorrect, demonstrating stable synchronization in homogeneous networks.

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Area of Science:

  • Physics
  • Network Science
  • Dynamical Systems

Background:

  • Synchronization is a common phenomenon in symmetrically coupled homogeneous oscillator networks.
  • Recent studies suggested stable synchronization requires heterogeneous oscillators in asymmetrically coupled networks.

Purpose of the Study:

  • To mathematically disprove the necessity of heterogeneous oscillators for stable synchronization in asymmetrically coupled networks.
  • To demonstrate the existence of stable synchronization states in homogeneous, asymmetrically coupled oscillator systems.

Main Methods:

  • Mathematical proof of synchronization conditions.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • Stable synchronization states exist in asymmetrically coupled homogeneous oscillator networks.
  • Previous conclusions regarding the necessity of heterogeneity for stable synchronization in such networks were mathematically incorrect.

Conclusions:

  • Asymmetric coupling does not preclude stable synchronization in homogeneous oscillator networks.
  • The study corrects and refines the understanding of synchronization phenomena in complex networks.