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Network susceptibilities: Theory and applications.

Debsankha Manik1, Martin Rohden2, Henrik Ronellenfitsch3,4

  • 1Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.

Physical Review. E
|February 18, 2017
PubMed
Summary
This summary is machine-generated.

We introduce network susceptibilities to measure how network dynamics change with small parameter alterations. This concept applies to various systems, including power grids and flow networks, aiding in understanding network behavior.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Dynamical Systems Theory

Background:

  • Understanding how complex networks respond to perturbations is crucial for their stability and function.
  • Existing methods often lack a unified framework to quantify collective dynamic responses to localized changes.

Purpose of the Study:

  • To introduce and define the concept of network susceptibilities.
  • To differentiate between vertex and edge susceptibilities for analyzing network responses.
  • To provide a generalized framework applicable to diverse network types.

Main Methods:

  • Derivation of explicit formulas for network susceptibilities in oscillator networks near steady states.
  • Application of the framework to Kuramoto-type phase-oscillator models.
  • Analysis of power grid models and generic flow models.

Main Results:

  • Defined vertex susceptibilities (response to unit property changes) and edge susceptibilities (response to interaction changes).
  • Derived analytical expressions for these susceptibilities in specific network models.
  • Demonstrated the applicability to oscillator, power grid, and flow networks.

Conclusions:

  • Network susceptibilities offer a powerful quantitative tool for analyzing the collective dynamics of complex systems.
  • The framework is generalizable to various network types, particularly those involving flow, transport, or spreading phenomena.
  • This concept is essential for understanding network responses to topological and parameter changes.