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This study explores how network structure influences synchronization in Kuramoto oscillator networks, revealing distinct behaviors in heterogeneous versus homogeneous networks. We analyze the interplay of mutual and driven synchronization, uncovering complex dynamics and bifurcations.

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Area of Science:

  • Complex Systems
  • Network Science
  • Non-equilibrium Dynamics

Background:

  • Synchronization is a key phenomenon in non-equilibrium systems.
  • Complex network studies often focus on how connectivity impacts system behavior.
  • Previous models emphasized mutual synchronization over external driving effects.

Purpose of the Study:

  • Investigate the interplay between mutual and driven synchronization in Kuramoto oscillator networks.
  • Examine how network topology affects synchronization states and their emergence.
  • Analyze dynamics in random networks with specified degree distributions.

Main Methods:

  • Modeling phase oscillators of the Kuramoto type.
  • Analyzing simple random networks with a given degree distribution.
  • Exploring parameter regions, particularly at weak coupling strengths.

Main Results:

  • Observed diverse dynamical behaviors, including bifurcations and bistability.
  • Found qualitative differences in dynamics between heterogeneous and homogeneous networks.
  • Identified a Takens-Bogdanov-Cusp singularity separating these behaviors.

Conclusions:

  • Network topology significantly shapes synchronization patterns in driven systems.
  • Heterogeneous and homogeneous networks exhibit distinct synchronization dynamics.
  • Understanding oscillator cluster dynamics is crucial for analyzing transitions and states.