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Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex
Maria Teodora Ferreira1, Rosangela Follmann1, Margarete O Domingues1
1Associated Laboratory for Computing and Applied Mathematics (LAC), Brazilian National Institute for Space Research (INPE), São José dos Campos 12227-010, Brazil.
Chaos (Woodbury, N.Y.)
|September 3, 2017
Summary
Detecting phase synchronization in coupled chaotic systems is challenging. This study introduces the Discrete Complex Wavelet Approach (DCWA) for accurate phase assignment, successfully analyzing experimental data from chaotic chemical processes.
Area of Science:
- Non-linear dynamics
- Complex systems analysis
- Signal processing
Background:
- Phase synchronization is a key phenomenon in coupled non-linear oscillators, crucial for understanding complex systems.
- Detecting phase synchronization, especially in non-phase-coherent chaotic systems, presents significant analytical challenges.
- Traditional methods often require state space reconstruction or extensive pre-processing, limiting their applicability.
Purpose of the Study:
- To introduce and validate the Discrete Complex Wavelet Approach (DCWA) for robust phase assignment in coupled chaotic systems.
- To demonstrate the effectiveness of DCWA in analyzing experimental data, particularly from non-phase-coherent chaotic processes.
- To highlight the advantages of DCWA in handling multi-scale properties for synchronization analysis.
Main Methods:
- Application of the Discrete Complex Wavelet Approach (DCWA), built upon the Dual-Tree Complex Wavelet Transform (DT-CWT).
- Analysis of scalar time series from coupled chaotic systems and experimental data.
- Evaluation of DCWA's performance without requiring state space reconstruction or pre-processing.
Main Results:
- DCWA accurately assigns phases and predicts phase synchronization in coupled chaotic systems.
- The method demonstrates high efficacy even with non-phase-coherent chaotic signals.
- Successful prediction of phase synchronization in a chemical experiment involving three coupled chaotic processes was achieved.
- The impact of different time-scales on synchronization was effectively analyzed, showcasing DCWA's multi-scale capabilities.
Conclusions:
- The Discrete Complex Wavelet Approach (DCWA) offers a powerful and efficient tool for detecting phase synchronization in complex systems.
- DCWA overcomes limitations of traditional methods by effectively analyzing scalar time series without pre-processing.
- The method's multi-scale analysis capabilities are advantageous for interpreting experimental data from coupled chaotic dynamics.
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