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Synchronization and desynchronization of self-sustained oscillators by common noise
Denis S Goldobin1, Arkady Pikovsky
1Department of Physics, University of Potsdam, Postfach 601553, D-14415 Potsdam, Germany.
Summary
External noise can synchronize identical limit cycle oscillators, but non-identities cause deviations. Large noise may desynchronize non-isochronous systems, as shown for the Van der Pol-Duffing model.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Statistical physics
Background:
- Limit cycle oscillators are fundamental in modeling periodic phenomena.
- External noise is a ubiquitous factor influencing dynamical systems.
- Understanding noise-induced synchronization and desynchronization is crucial for many applications.
Purpose of the Study:
- To investigate the impact of external white noise on limit cycle oscillator dynamics.
- To analytically study the effects of system non-identities and noise variations.
- To characterize deviations from perfect synchrony and identify conditions for desynchronization.
Main Methods:
- Analysis of Lyapunov exponents to determine system stability and synchronization.
- Analytical derivations for small non-identities in oscillators and noise.
- Statistical analysis of synchronization deviations.
- Numerical demonstration using the Van der Pol-Duffing oscillator model.
Main Results:
- Small white noise induces synchronization in identical oscillators (negative Lyapunov exponent).
- Non-identities in oscillators or noise lead to statistical deviations from perfect synchrony.
- Large white noise can cause desynchronization in non-isochronous systems.
- The Van der Pol-Duffing system exhibits noise-induced desynchronization.
Conclusions:
- External noise plays a dual role in oscillator synchronization, promoting it for identical systems and potentially disrupting it for non-identical or non-isochronous systems.
- The study provides analytical tools to predict and understand noise effects on coupled oscillators.
- Non-isochronicity is a key factor for large noise-induced desynchronization.
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