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Spectral energy transfer on complex networks: a filtering approach
Theodore MacMillan1, Nicholas T Ouellette2
1Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, 94305, USA.
Scientific Reports
|September 5, 2024
Summary
Networked nonlinear oscillators show spectral energy transfer, similar to turbulence. A new method localizes these interactions, revealing how network structure impacts energy flow.
Area of Science:
- Complex Systems
- Network Science
- Fluid Dynamics
Background:
- Spectral analysis is key for understanding dynamical systems and phenomena like turbulent energy cascades.
- Networked dynamical systems offer reduced-order models but often sacrifice interpretability and locality.
- Existing methods struggle to localize network interactions.
Purpose of the Study:
- To demonstrate spectral energy transfer in a network of nonlinear oscillators.
- To introduce a method for localizing higher-order interactions within the network.
- To investigate the influence of local network topology on these interactions.
Main Methods:
- Analysis of spectral energy transfer in nonlinear oscillator networks.
- Application of a filter-based decomposition inspired by large eddy simulation.
- Investigation of local network topology effects.
Main Results:
- A network of nonlinear oscillators exhibits spectral energy transfer via an effective force analogous to Reynolds stress.
- Higher-order interactions were successfully localized to individual nodes using the filter-based decomposition.
- Local topology was shown to influence these emergent higher-order interactions.
Conclusions:
- Spectral energy transfer is an emergent property in networked nonlinear oscillators.
- The developed method allows for the localization and study of these interactions.
- Network topology plays a crucial role in shaping emergent higher-order dynamics.
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