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Continuous wavelet transform in the analysis of burst synchronization in a coupled laser system
A Bergner1, R Meucci, K Al Naimee
1Center for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
This study numerically investigates coupled chaotic carbon dioxide (CO2) lasers, finding that increasing coupling strength enhances synchronization differently across various frequencies. The complex continuous wavelet transform method effectively analyzes synchronization in complex systems.
Area of Science:
- Nonlinear dynamics
- Laser physics
- Chaos theory
Background:
- Coupled chaotic lasers exhibit complex behaviors, including bursting with varying frequencies.
- Analyzing synchronization in systems with multiple time scales is challenging.
Purpose of the Study:
- To numerically investigate the transition to synchronization in a model of coupled chaotic carbon dioxide (CO2) lasers.
- To develop and apply a robust method for synchronization analysis in complex time series.
Main Methods:
- Numerical modeling of a coupled chaotic CO2 laser system.
- Application of complex continuous wavelet transform (CCWT) for synchronization analysis.
- CCWT enables simultaneous resolution of event frequency and occurrence time, and phase estimation.
Main Results:
- The system displays bursting episodes with different predominant frequencies.
- Synchronization analysis using CCWT revealed that mutual coherency increases non-uniformly with coupling strength across different frequencies.
- The CCWT method was validated using experimental data.
Conclusions:
- The complex continuous wavelet transform is a powerful tool for analyzing synchronization in multi-timescale chaotic systems.
- Synchronization in coupled chaotic CO2 lasers is frequency-dependent.
- The findings provide insights into controlling and understanding synchronization in complex laser systems.
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