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Estimation of delay in coupling from time series.
Laura Cimponeriu1, Michael Rosenblum, Arkady Pikovsky
1Department of Medical Physics, University of Patras, 26 500 Rion Patras, Greece.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
Summary
Estimating time delays in coupled oscillators is possible using phase dynamics analysis. Irregularity in phase dynamics, from noise or chaos, is crucial for accurate time delay determination between coupled oscillators.
Area of Science:
- Nonlinear dynamics
- Complex systems analysis
- Time series analysis
Background:
- Coupled oscillators are fundamental in various scientific fields.
- Estimating coupling delays is essential for understanding system dynamics.
- Traditional methods like cross-correlation have limitations.
Purpose of the Study:
- To develop and validate methods for estimating time delays in weakly coupled oscillators.
- To investigate the role of phase dynamics irregularity in delay estimation.
- To compare novel methods with standard cross-correlation analysis.
Main Methods:
- Analysis of interrelations between signal phases from time series data.
- Development of two novel phase-based methods for time delay estimation.
- Analytical and numerical simulations to verify method performance.
- Comparison with standard cross-correlation techniques.
Main Results:
- Successful estimation of time delays in weakly coupled self-sustained oscillators.
- Demonstrated the necessity of phase dynamics irregularity (noise or chaos) for accurate delay determination.
- Showcased the advantages of the proposed methods over cross-correlation analysis.
Conclusions:
- Novel phase-based methods effectively estimate time delays in coupled oscillators.
- Phase dynamics irregularity is a key factor for successful delay estimation.
- These methods offer an improved approach for analyzing coupled oscillatory systems.