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\subsection{Deterministic and 2:1 mode locking}  To investigate whether our system can adopt different mode locked state, we drew the Arnold tongue of the deterministic model. The presence of synchronized regions (black, Figure \ref{fig:arnold}A) at each rational number $T_2/T_1 = p/q$ shows that this is the case, also reflecting the pulsed (i.e. localized in the phase plane) nature of the inferred coupling.  To test if cells could adopt different mode locked states, we estimated the $2:1$ attractor from the deterministic model (blue, Figure \ref{fig:arnold}B) and computed for each trace the average distance to the attractor. We found that a fraction of the cell closely follow the $2:1$ attractor as illustrated in Figure \ref{fig:arnold}B-D). In total about $7%$ $7\%$  of the cell traces were closer to the $2:1$ attractor than to the $1:1$. This indicates that cells with long cell cycle durations can adopt a $2:1$ mode locked state where the cell divides every two circadian peaks. However, the length of our recordings and the stochastic nature of the processes make difficult to distinguish between more complicated scenario (e.g. $3:2$ vs $1:1$) $1:1$).