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| Synchronization of biological clocks is a well studied topic. We will address the question how noise in general affects synchronization before turning to a system of two coupled oscillators.
In the absence of noise and for sufficiently strong coupling, synchronization is observed (the oscillators are \q\q in phase\rq\rq). In the presence of small noise, the system will still spend most of the time in metastable equilibrium, i.e., the difference in phase will show only small fluctuations. However, occasionally transitions to other metastable states are observed. Such transitions can by viewed as a \lq\lq phase slips\rq\rq. We will derive an expression for probability distribution of phase slips, thereby uncovering universal properties of the distribution. |
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