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Synchronization of spectral components and its regularities in chaotic dynamical systems
Alexander E Hramov1, Alexey A Koronovskii, Mariya K Kurovskaya
1Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya, 83, Saratov 410012, Russia. aeh@cas.ssu.runnet.ru
Summary
This study explores chaotic synchronization in coupled systems, revealing that synchronization emerges from phase relationships in Fourier spectra. A universal power law governs this spectral component synchronization.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Coupled dynamical systems exhibit complex behaviors, including synchronization.
- Understanding the onset of chaotic synchronization is crucial for analyzing system interactions.
Purpose of the Study:
- To investigate the mechanism behind the onset of chaotic synchronization in coupled systems.
- To define criteria and measures for synchronization of spectral components.
- To describe the universal power law governing this phenomenon.
Main Methods:
- Analysis of frequency components in Fourier spectra of coupled chaotic oscillators.
- Development of a synchronization criterion and measure for spectral components.
- Empirical validation using coupled Rössler, Van der Pol, and Van der Pol-Duffing systems.
Main Results:
- Synchronization onset is linked to phase relations between oscillator frequency components.
- A criterion and measure for spectral component synchronization were established.
- A universal power law describing synchronization was identified and illustrated.
Conclusions:
- Phase relations in Fourier spectra are fundamental to chaotic synchronization.
- The identified power law offers a generalized understanding of synchronization dynamics.
- The findings are applicable to various coupled nonlinear oscillator systems.