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We developed a formula to predict synchronizability in complex networks using eigenratios and costs. This method efficiently assesses how networks synchronize, regardless of their structure or oscillator properties.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Synchronizability is crucial for understanding emergent behavior in coupled oscillator systems.
  • Assessing synchronizability in large, complex networks often requires computationally intensive methods.

Purpose of the Study:

  • To introduce a general formula for determining synchronizability in large, randomized, and weighted simplicial complexes.
  • To provide an efficient method for assessing and manipulating network synchronizability.

Main Methods:

  • Utilizing eigenratios and costs to predict complete synchronizability.
  • Systematically varying coupling strengths, degree distributions, and intensity distributions.
  • Employing diffusive couplings in randomized weighted simplicial complexes.

Main Results:

  • Eigenratios and costs reliably gauge synchronizability across diverse network topologies and intensity distributions.
  • The formula eliminates the need for explicit connectivity matrices and eigenvalue calculations.
  • Synchronizability can be manipulated by adjusting degrees, weights, and coupling strengths.

Conclusions:

  • The proposed formula offers an efficient and general approach to synchronizability analysis in complex systems.
  • The findings are validated using simplicial complexes of Rössler oscillators and are independent of system size and specific distributions.
  • The method is applicable to systems with higher-order interactions and real-world network topologies.