Fig. 2

Patterns of variables x, y, and Ca generated by system (1a)–(1c) with different values of μ. The orbits correspond to types A, B and C described in the text and illustrated in Fig. 1. The other parameter values were chosen according to Table 1. a ($\mu =2$): system (1a)–(1c) admits an attractive limit cycle of relaxation type. The increase in the calcium level is triggered by the activation of x, the decrease by its deactivation. The Ca pattern is oscillatory and consists of successive peaks without any quiescent phase between two successive peaks. b ($\mu =2.4$): system (1a)–(1c) admits an attractive MMO limit cycle. The quiescent phase after each Ca peak is due to small oscillations of the current point near the fold ${\mathcal{F}}^{-}$, which results in a slight and slow increase in Ca before the subsequent peak. The Ca pattern fulfills the average quantitative specifications provided by the experimental data. c ($\mu =3$): starting from an initial condition just below the fold ${\mathcal{F}}^{-}$, the Ca pattern consists of a unique peak. Afterward, the current point $(x,y,\mathrm{Ca})$ tends asymptotically to a stable steady state