## 4 Discussion  
In this paper, we present the integration of AdEx mean-field models into whole-cortex simulations for three species: mice, monkeys, and humans. The chosen model is  
Figure 5: Comparison of the asynchronous and synchronized slow-wave dynamics in mouse, macaque, and human brain models. (**A**) Transition between asynchronous and slow-wave dynamics measured by the mean duration of down states. (**B**) Mean phase-lag index (PLI) for excitatory neuron activities for the three species. (**C**) Same as B, but with the connection delays matched between the three connectomes. a second-order mean-field model, grounded in biophysically plausible spiking models, built using a bottom-up approach. The model is able to reproduce the asynchronous and slow oscillatory states of neural networks and therefore permits us to evaluate the emergence of synchronized slow waves at the whole-brain level across three distinct species. For each species, the simulations exhibit the main features of the TVB-AdEx model, as found earlier [13,14]. In particular, the three models exhibit the same emerging property found in human brain simulations, namely that when the individual AdEx nodes are set to asynchronous mode, the ensemble of nodes remains asynchronous. This mode of activity is consistent with the \"desynchronized\" activity classically found in the awake human brain [1,2]; this is also seen in both human and monkey brains in microelectrode recordings, which also display asynchronous irregular states [28]. Similarly, when the AdEx nodes are in the up-down state, the activity across the whole cortex synchronizes into a slow oscillatory mode. Moreover, this slow oscillatory mode corresponds to the up-down states seen in single units in microelectrode recordings of humans and monkeys during slow-wave sleep [28,29]. Microelectrode recordings in mice also display the same two states--asynchronous irregular dynamics during wakefulness and up-down state dynamics during slow-wave sleep [30]; the same can be seen in cats [31]. We believe that the simulations explored here, and in those for which we provide Python code [32], constitute a very useful tool for the community of computational neuroscientists interested in simulating whole-brain dynamics in mice, monkeys, and humans. We must note here that the codes we provide are run within the TVB environment [24]. In addition, we have also implemented versions of these models that can be run online, on the EBRAINS platform. This will allow users to run the models and change the parameters without even installing TVB, which may also be a useful tool. Finally, we would like to mention a few possible limitations and extensions to the models explored here. The connectomes used in our study have been derived from different experimental methods (axonal tract-tracing, diffusion weighted images, or a combination of both) and they may exhibit discrepancies in terms of spatial resolution, sensitivity, and accuracy due to inherent differences in the underlying data acquisition and processing procedures. As a direct implication, the connectomes lack consistent directionality (since diffusion-weighted imaging does not provide this information), which may have an effect on the connectivity patterns and their emergent dynamics. It is also important to keep in mind that these are purely cortical models, ignoring the contribution of subcortical structures in the generation of slow-wave activity, with rather coarse brain parcellations that include less than a hundred regions for each species. A first suggested extension to this study is thus to complete the present model, which is only cortical, by including other regions, such as the thalamus, hippocampus, basal ganglia, or cerebellum. Integrating these regions will require the design of mean-field models specific to each brain region, which was achieved recently for the cerebellum [33] and thalamus [34], and is in progress for other brain regions.