Interplay between couplings and common noise in phase synchronization: disagreement between global analysis and local stability characterization
Abstract
We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the "effective coupling" is big compared to the common noises, the former favors and the latter hinder synchronization. On the contrary, when the coupling is small compared to the proportional noises, we find that the latter induce synchronization, optimally when their intensities are big and in the n:m synchronization ratio. Furthermore, in such case a small value of the coupling is better for synchronization. Finally, we show that synchronization, which is a global property, must not be studied via local stability such as with Lyapunov exponents.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2008
- DOI:
- 10.48550/arXiv.0809.2398
- arXiv:
- arXiv:0809.2398
- Bibcode:
- 2008arXiv0809.2398G
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems
- E-Print:
- 5 pages, 4 figures, revtex. Added an example that shows that synchronization, which is a global property, must not be studied by means of a local stability analysis such as via Lyapunov exponents. Other changes of medium importance were made as well