Directed recurrence networks for the analysis of nonlinear and complex dynamical systems.
Rémi Delage1, Toshihiko Nakata1
1Department of Management Science and Technology, Tohoku University, Sendai 980-8579, Japan.
Chaos (Woodbury, N.Y.)
|January 3, 2025
Summary
Directed recurrence networks offer a novel approach to analyzing complex dynamical systems. Spectral analysis of these networks reveals crucial information about system dynamics, complexity, and stability.
Area of Science:
- Dynamical Systems Analysis
- Network Science
- Time Series Analysis
Background:
- Complex network approaches are increasingly used for dynamical system analysis.
- Reconstruction methods from time series reveal complex behaviors via network topology.
- Directed recurrence networks (DRNs) complement existing recurrence networks.
Purpose of the Study:
- Investigate the performance of directed recurrence networks for nonlinear and complex dynamical systems.
- Compare DRNs with Markov chain approximations of the transfer operator.
- Highlight the advantages of the DRN approach.
Main Methods:
- Utilized directed recurrence networks for time series analysis.
- Performed spectral analysis on the constructed networks.
- Compared DRN results with Markov chain approximations.
Main Results:
- DRNs show strong parallels with Markov chain approximations but possess distinct structural differences.
- Spectral analysis of DRNs provides crucial insights into system complexity, dynamical patterns, and stability.
- DRNs preserve data resolution and offer a well-defined recurrence threshold.
Conclusions:
- Directed recurrence networks are a valuable tool for analyzing complex dynamical systems.
- Spectral analysis of DRNs offers a powerful method for understanding system dynamics.
- DRNs present advantages in data resolution and threshold definition for recurrence analysis.
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