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Area of Science:

  • Complex Systems
  • Network Science
  • Dynamical Systems

Background:

  • Complex networks exhibit heterogeneity in node properties and their impact on global dynamics.
  • Synchronized states in networks of coupled phase oscillators serve as a baseline for analysis.
  • Perturbations to intrinsic node parameters can disrupt synchronization, leading to new phase-locked states.

Purpose of the Study:

  • To quantify the functional response of complex networks to local perturbations using phase dispersion.
  • To introduce a modified Kuramoto model with node-dependent frustration parameters to study network behavior.
  • To define and compute a node characteristic, 'functionability', based on network topology and perturbation response.

Main Methods:

  • Proposed a phase dispersion measure to quantify system response to local perturbations.
  • Implemented a variation of the Kuramoto model incorporating node-specific frustration parameters.
  • Analyzed the dependence of stationary phase-locked states on frustration parameters and network topology.

Main Results:

  • The stationary state of the network depends on individual node frustration parameters and overall topology.
  • Phase dispersion quantifies the network's response, influenced by topology and the perturbed node.
  • A node's 'functionability' can be analytically computed from network topology.

Conclusions:

  • Node-dependent frustration parameters significantly alter network dynamics and phase-locked states.
  • The proposed 'functionability' metric offers a topology-based characterization of nodes within complex networks.
  • The study provides a novel approach to analyzing network response and node importance, with comparisons to centrality measures.