Fig. 4

Transition of the j th cell of the network from independent to synchronized regime. In each panel, the blue parts correspond to the unsynchronized regime, $\sigma <{\sigma }_{\mathrm{on}}$ and ${\varphi }_{\mathrm{syn}}(\sigma )\simeq 0$, and the red parts to the synchronized regime, $\sigma >{\sigma }_{\mathrm{on}}$ and ${\varphi }_{\mathrm{syn}}(\sigma )\simeq 1$. a and b represent the projection of the orbit onto the plane $(x_j,y_j)$ for $\sigma <{\sigma }_{\mathrm{on}}$ and $\sigma >{\sigma }_{\mathrm{on}}$, respectively, and the position of the $x_j$ and $y_j$ nullclines. The $x_j$ nullcline depends on ${\mathrm{Ca}}_j$: in each panel, the two cubic curves represent the $x_j$ nullcline for the minimal (lower curve) and maximal (upper curve) value taken by ${\mathrm{Ca}}_j$ during the corresponding regime. c to f represent the generated $x_j$, ${\mathrm{Ca}}_j$, mean calcium (among all cells) and σ patterns. As long as $\sigma <{\sigma }_{\mathrm{on}}$, each cell generates a ${\mathrm{Ca}}_j$ pattern with it owns rhythm: the cells are asynchronous and the mean calcium level remains low (blue parts). When σ exceeds ${\sigma }_0$ (red parts), ${\varphi }_{\mathrm{syn}}(\sigma )$ is activated and the cells for which ${\eta }_i$ is large enough enter the steady regime (b). Hence, they produce, all almost at the same time, a higher calcium peak than in the asynchronous period of the oscillation. The mean calcium level exceeds ${\mathrm{Ca}}_{\mathrm{desyn}}$, which resets σ to a value close to ${\sigma }_0$