Fig. 7

Synchronization as doublets in patterns of calcium oscillations in the 50 GnRH cells of a network. The parameter values of system (6a)–(6d) are given in Tables 1 and 3. In a, ten different colors have been used to represent the ${\mathrm{Ca}}_j$ patterns, hence each color is used to represent the activity of 5 individual cells. b represents the corresponding patterns of σ as well as the synchronization threshold ${\sigma }_{\mathrm{on}}$ (dotted line). c represents the mean calcium level $\frac{1}{N}{\sum }_{i=1}^N{\mathrm{Ca}}_i$ as well as the threshold ${\mathrm{Ca}}_{\mathrm{desyn}}$ (dotted line) which triggers the decrease of σ. Doublets of synchronization occur at minutes 19–26 and minutes 78–86: the two first episodes of synchronization are separated by a 60 minute period. The doublets occur because, after the first episode has been triggered, the mean calcium value stays above the threshold ${\mathrm{Ca}}_{\mathrm{desyn}}$ only during a short time and, since the γ value is small, σ starts increasing again before reaching ${\sigma }_0$ vicinity. Consequently, the subsequent synchronization episode occurs only 7 minutes afterward. It is worth noticing that the synchronization during the second episode of each doublet is tighter than during the first one. Hence, the subsequent decrease in σ is stronger than the preceding one, which results into a 56 minute period before the following doublet