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Reconstruction of a system's dynamics from short trajectories
C Komalapriya1, M Thiel, M C Romano
1Center for Dynamics of Complex Systems, University of Potsdam, 14415 Potsdam, Germany. komala@agnld.uni-potsdam.de
Summary
Researchers can reconstruct long time series from short segments using phase space recurrences. This method enables understanding system dynamics even with limited data acquisition, crucial for time series analysis.
Area of Science:
- Dynamical systems theory
- Time series analysis
- Nonlinear dynamics
Background:
- Time series analysis requires long datasets to accurately model system dynamics.
- Acquiring extensive time series data is frequently impractical.
- Understanding system behavior with limited data is a significant challenge.
Purpose of the Study:
- To investigate the feasibility of reconstructing complete system dynamics from numerous short time series.
- To develop a method for generating a single, long time series from short segments.
- To determine if the reconstructed time series accurately reflects the underlying system's dynamics.
Main Methods:
- Utilizing the concept of recurrences in phase space.
- Generating a single long time series by concatenating short time series segments.
- Ensuring the reconstructed time series exhibits dynamics similar to the original system.
Main Results:
- A method was successfully developed to construct a long time series from short observational data.
- The generated long time series demonstrates dynamics comparable to those of an actual long time series.
- This approach offers a viable solution for analyzing systems with limited data availability.
Conclusions:
- It is possible to understand complete system dynamics from multiple short time series.
- Phase space recurrences provide a powerful tool for time series reconstruction.
- The proposed method enhances the applicability of time series analysis in data-scarce scenarios.
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