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Clustering coefficient and periodic orbits in flow networks.

Victor Rodríguez-Méndez¹, Enrico Ser-Giacomi², Emilio Hernández-García¹

¹IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.

Chaos (Woodbury, N.Y.)

|April 3, 2017

Summary

Network theory

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Area of Science:

Fluid dynamics and network theory
Dynamical systems analysis

Background:

Network theory offers tools to analyze complex systems.
Flow networks represent fluid transport, with links indicating fluid movement.

Purpose of the Study:

To investigate the application of the clustering coefficient in flow networks.
To determine if network measures can identify periodic trajectories in fluid flows and dynamical systems.

Main Methods:

Constructing flow networks from fluid flow data using a time interval τ.
Applying the clustering coefficient measure to these networks.
Analyzing network properties for different flow types (steady, periodic, turbulent).
Performing a 'spectroscopy' by varying τ to identify periodic orbits.

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Main Results:

The clustering coefficient accurately identifies approximate locations of periodic trajectories in flow systems.
This holds true for steady and periodic flows when τ matches the flow period or its multiple.
The method also detects cyclic motion in other situations.
Varying τ reveals periodic orbits of period 3τ through high mean clustering values.

Conclusions:

The clustering coefficient is a valuable tool for detecting periodic behavior in fluid flows and general dynamical systems.
Network-based 'spectroscopy' by varying τ can uncover hidden periodic orbits.
This approach provides insights into the phase space dynamics of complex systems.