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Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices
M Tyloo1,2, T Coletta1, Ph Jacquod1
1School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, CH-1951 Sion, Switzerland.
Physical Review Letters
|March 16, 2018
Summary
Assessing network vulnerability is crucial. New generalized Kirchhoff indices offer a fast, reliable method to evaluate network resilience against perturbations by analyzing stability matrices and eigenmodes.
Area of Science:
- Network theory
- Complex systems
- Dynamical systems
Background:
- Assessing network vulnerability is a key challenge in network theory.
- Understanding how complex networks respond to external perturbations is essential for reliability.
Purpose of the Study:
- To develop a fast and reliable method for assessing network vulnerability.
- To investigate the response of synchronous states in coupled dynamical systems on complex networks to external perturbations.
Main Methods:
- Analysis of eigenvalues and eigenmodes of the stability matrix for unperturbed dynamics.
- Introduction and application of generalized Kirchhoff indices derived from averaged perturbation responses.
- Investigating specific, non-averaged perturbations and their impact on synchronous states.
Main Results:
- Network response to specific perturbations depends on stability matrix eigenvalues and eigenmode overlaps.
- New graph topological indices, generalized Kirchhoff indices, are introduced.
- These indices provide a measure of network vulnerability based on averaged perturbation responses.
Conclusions:
- The generalized Kirchhoff indices offer a computationally efficient and accurate approach to network vulnerability assessment.
- This method enables rapid evaluation of network resilience against various threats, including faults and attacks.
- Findings contribute to the design and maintenance of robust complex networks.
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