Model-based indicators
We fitted threshold AR(p ) models (p [1,3]) and found that the best fitting model was AR(3) (Fig. 3). For female data, the models’ fit were worse for p = 1 (ΔAIC = 1242) and p = 2 (ΔAIC = 14), similar to the male data (p = 1 (ΔAIC = 2630) andp = 2 (ΔAIC = 15)). The fit of the threshold AR(3) model was statistically better than that of a simple AR(3) model for the female (\(\chi_{3}^{2}+\chi_{4}^{2}=\) 51.63, P < 0.001) and the male (\(\chi_{4}^{2}+\chi_{5}^{2}=\) 70.56, P< 0.001). AR(p ) models also showed that air temperature explained an important part of the deviance in body temperatures, especially during hibernation, when body temperature was highly synchronous with air temperature (Appendix S1, Table S4). The fitted model showed that there were alternative states between the activity and the hibernation states, separated by unstable saddle points that corresponded to flickering temperature causing a region of bistability (Fig. 4). The potential landscape confirmed the occurrence of flickering and of two minima (stable states) separated by a local maximum (unstable equilibrium) (Fig. 4). The potential was lower and more narrow (lower temperature range) for Te during normal activity than for the hibernation temperature, and it showed a similar pattern for the two studied dormice. Switches between hibernation and activity occurred at different critical conditions of temperature, which was indicative of hysteresis. In late spring, dormice awoke at higher air temperatures than air temperature when they entered hibernation in late autumn (Fig. 5).