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In the deterministic case ($\sigma_i=0$) the two phase can adopt synchronized solutions in which the deterministic attractor, a close curved in the plane, will attract all trajectories. In addition, the system can adopt different mode of synchronization. In $1:1$ mode-locking the two oscillators will oscillate with the same average frequency, while in $2:1$ mode-locking the first oscillator will run twice as fast as the second one. In general, depending on the coupling functions, any $p:q$ mode-locking can exist, where $p$ and $q$ are integers.  In the presence of a small amount of noise, synchronization will be manifested by non-uniform distribution of trajectories in the plane, centered around the deterministic attractor. In this case synchronization is often characterized by looking at the distribution of one of the phase for a fixed value of the second one, for example the circadian phase at division (i.e. the distribution of $\theta(t_d)$ with $t_d : \phi(t_d) = 2\pi$) \ref{bieler2014,Feillet2014}. \ref{bieler2014},\ref{Feillet2014}.  A unimodal distribution indicates $1:1$ mode-locking, a bimodal distribution $1:2$ mode-locking (two divisions during one circadian cycle) while a uniform distribution indicates an unsynchronized state. The degree of synchronization between two stochastic oscillators can also be measured by the synchronization index $R(\theta_t-\phi_t) = | 1/N\sum_{k=1}^N \exp(i\theta_k - i\phi_k) |$ that can take values from zero (no synchronization) to one (perfect synchronization).